*On some imbeddings of lattices into the normal lattices*, Bull. Acad. Pol. Sci., Ser. sci. math., astr. et phys.**17**(1969), 431--436*On expanding maps of compact manifolds and local homeomorphisms of a circle*, ibid.**18**(1970), 725--732*On non-continuity of topological entropy*, ibid.**19**(1971), 319--320*Diffeomorphism without any measure with maximal entropy*, ibid.**21**(1973), 903--910*Topological conditional entropy*, Studia Math.**55**(1976), 175--200*A short proof of the variational principle for a Z^N_+ action on a compact space*, Asterisque**40**(1976), 147--157*Entropy of piecewise monotone mappings*(with W. Szlenk), ibid.**50**(1977), 299--310 (this is a short version of 13.)*Topological entropy and degree of smooth mappings*(with F. Przytycki), Bull. Acad. Pol. Sci., Ser. sci. math., astr. et phys.**25**(1977), 573--574*Entropy conjecture for tori*(with F. Przytycki), ibid., 575--578*Horseshoes for mappings of the interval*, ibid.**27**(1979), 167--169 (this is a short version of 11.)*Horseshoes for continuous mappings of an interval*, in "Dynamical Systems", Liguori Editore, Napoli 1980, pp. 127--135*Invariant measures for continuous transformations of [0,1] with zero topological entropy*, in "Ergodic Theory" (Lecture Notes in Math.**729**), Springer, Berlin 1979, pp. 144--152*Entropy of piecewise monotone mappings*(with W. Szlenk), Studia Math.**67**(1980), 45--63*Existence of a homoclinic point for the Henon map*(with B. Szewc), Commun. Math. Phys.**75**(1980), 285--291*Strange attractors for the Lozi mappings*, Ann. New York Acad. Sci.**357**(1980) ("Nonlinear Dynamics"), 348--358*Periodic points and topological entropy of one dimensional maps*(with L. Block, J. Guckenheimer and L.-S. Young), in "Global Theory of Dynamical Systems", (Lecture Notes in Math.**819**), Springer, Berlin 1980, pp. 18--34*Structure of mappings of an interval with zero entropy*, Publ. Math. IHES**53**(1981), 5--16*Absolutely continuous measures for certain maps of an interval*, ibid., 17--51*On iterates of e^z*, Ergod. Th. & Dynam. Sys.**1**(1981), 103--106*Hopf's theorem on invariant measures for a group of transformations*(with D. Ramachandran), Studia Math.**74**(1982), 183--189*Topological entropy and metric entropy*, in "Theorie Ergodique", L'Enseigment Math., Geneve 1981, pp. 61--66*The result of Rafal Kolodziej*, ibid., pp. 57--60*Odd chaos*(with T.-Y. Li, G. Pianigiani and J. Yorke), Phys. Lett. A**87**(1982), 271--273*No division implies chaos*(with T.-Y. Li, G. Pianigiani and J. Yorke), Trans. Amer. Math. Soc.**273**(1982), 191--199*Periodic points of maps of degree one of a circle*, Ergod. Th. & Dynam. Sys.**2**(1982), 221--227*Perturbations and transitivity for certain maps of an interval*, ibid., 229--240*Attracting Cantor set of positive measure for a C^infinity map of an interval*, ibid., 405--415*Maps of an interval*, in "Chaotic behaviour of deterministic systems", North-Holland 1983, pp. 565--590*Twist sets for maps of the circle*, Ergod. Th. & Dynam. Sys.**4**(1984), 391--404*Convergence of images of certain measures*(with A. Zdunik), in "Statistical Physics and Dynamical Systems" (Progress in Phys.**10**), Birkhauser 1985, pp. 203--219*Embedding inverse limits of interval maps as attractors*, Fundam. Math.**125**(1985), 23--40*One-dimensional dynamical systems*, in "Proceedings of International Congress of Mathematicians, Warszawa 1983", PWN 1984, pp. 1277--1281*Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point*(with Ll. Alseda, J. Llibre and C. Simo), Ergod. Th. & Dynam. Sys.**5**(1985), 501--517*Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point*(with Ll. Alseda, J. Llibre and C. Simo), in: Actas VII Congr. Ecuac. Diff. y Appl., Univ. de Granada 1985 (this is a short version of 33.)*Dimension of invariant measures for maps with exponent zero*(with F. Ledrappier), Ergod. Th. & Dynam. Sys.**5**(1985), 595--610*Rotation intervals for a class of maps of the real line into itself*, ibid.,**6**(1986), 117--132*Chaos almost everywhere*, in "Iteration Theory and its Functional Equations" (Lecture Notes in Math.**1163**), Springer, Berlin 1985, pp. 125--130*Remark on the definition of topological entropy*, in "Dynamical Systems and Partial Differential Equations", Caracas 1986, pp. 65--68*Rate of convergence for computing entropy of some one-dimensional maps*(with K. Ziemian), in "Ergodic Theory and Related Topics II", (Teubner-Texte zur Math.**94**), Leipzig 1987, pp. 147--159*Lower bounds of the topological entropy for continuous maps of the circle of degree one*(with Ll. Alseda, J. Llibre and F. Manosas), Nonlinearity**1**(1988), 463--479*Smooth chaotic maps with zero topological entropy*(with J. Smital), Ergod. Th. & Dynam. Sys.**8**(1988), 421--424*Primary cycles on the circle*(with L. Block, E. Coven and L. Jonker), Trans. Amer. Math. Soc.**311**(1989), 323--335*Jumps of entropy in one dimension*, Fundam. Math.**132**(1989), 215--226*Periodic orbits of maps of Y*(with Ll. Alseda and J. Llibre), Trans. Amer. Math. Soc.**313**(1989), 475--538*Periodic and strange attractors in a model of a chemical system*(with A.L. Kawczynski and K.W. Leszczynski), Polish J. Chem.**63**(1989), 239--247*Absolutely continuous invariant measures for maps with flat tops*(with M. Benedicks), Publ. Math. IHES**69**(1989), 203--213*On n numbers on a circle*(with A. Schinzel), Hardy - Ramanujan Journal**11**(1988), 30--39*Formalism for studying periodic orbits of one dimensional maps*, in "European Conference on Iteration Theory (ECIT 87)", World Scientific, Singapore 1989, pp. 1--7*Cycles for degree -1 circle maps*(with K. Ziemian), in "European Conference on Iteration Theory (ECIT 87)", World Scientific, Singapore 1989, pp. 8--25*Topological entropy for circle maps of degree one*(with Ll. Alseda, J. Llibre and F. Manosas), in "European Conference on Iteration Theory (ECIT 87)", World Scientific, Singapore 1989, pp. 382--391 (this is a short version of 40.)*Persistent rotation intervals for old maps*, in "Dynamical Systems and Ergodic Theory", Banach Center Publ.**23**, PWN, Warsaw 1989, pp. 119--124*Rigid sets in the plane*(with J. Aaronson and S. Glasner), Israel J. Math.**68**(1989), 307--326*Periods and entropy for Lorenz-like maps*(with Ll. Alseda, J. Llibre and C. Tresser), Ann. Inst. Fourier**39**(1989), 929--952*Rotation sets of toral flows*(with J. Franks), Proc. Amer. Math. Soc.**109**(1990), 243--249*Rotation sets for maps of tori*(with K. Ziemian), J. London Math. Soc. (2)**40**(1989), 490--506*At the other side of a saddle-node*(with A. L. Kawczynski), Commun. Math. Phys.**131**(1990), 605--617*Period adding phenomenon in 1D return maps*(with A. L. Kawczynski), Z. Phys. Chemie (Leipzig)**271**(1990) 5, 1037--1046*Monotonicity properties of the family of trapezoidal maps*(with K. Brucks and C. Tresser), Commun. Math. Phys.**137**(1991), 1--12*Roots of continuous piecewise monotone maps of an interval*(with A. Blokh, E. Coven and Z. Nitecki), Acta Math. Univ. Comenianae**60**(1991), 3--10*Rotation sets and ergodic measures for torus homeomorphisms*(with K. Ziemian), Fundam. Math.**137**(1991), 45--52*Entropy of piecewise continuous interval maps*(with S. V. Shlyachkov), in "European Conference on Iteration Theory, ECIT 89", World Scientific, Singapore, 1991, pp. 239--245*Pushing inward*, in "European Conference on Iteration Theory, ECIT 89", World Scientific, Singapore, 1991, pp. 371--375*Combinatorial patterns for maps of the interval*(with Z. Nitecki), Mem. Amer. Math. Soc.**94**(1991), no. 456*Kneading sequences of skew tent maps*(with E. Visinescu), Ann. Inst. H. Poincare, Probab. Stat.**27**(1991), 125--140*Periodic orbits for interval maps with sharp cusps*(with A. L. Kawczynski), Physica D**52**(1991), 191--203*Comparing periodic orbits of maps of the interval*(with C. Bernhardt, E. Coven and I. Mulvey), Trans. Amer. Math. Soc.**333**(1992), 701--707*Entropy of snakes and the restricted variational principle*(with J. Tolosa), Ergod. Th. & Dynam. Sys.**12**(1992), 791--802*Horseshoes and entropy for piecewise continuous piecewise monotone maps*(with K. Ziemian), in "From phase transitions to chaos", World Scientific, Singapore 1992, pp. 489--500-
*Combinatorial Dynamics and Entropy in Dimension One*(with Ll. Alseda and J. Llibre), World Scientific (Advanced Series in Nonlinear Dynamics, vol. 5) 1993, Second Edition 2000 *Horseshoes, entropy and periods for graph maps*(with J. Llibre), Topology**32**(1993), 649--664*Unimodal interval maps obtained from the modified Chua equations*, Internat. J. Bifur. Chaos Appl. Sci. Engrg.**3**(1993), 323--332*Cycles for disk homeomorphisms and thick trees*, (with J. Franks), in "Nielsen Theory and Dynamical Systems Conference Proceedings", Contemporary Math.**152**(1993), 69--139*Minor cycles for interval maps*, Fundam. Math.**145**(1994), 281--304*Rotation numbers of projectivities*(with M. Frantz), J. Math. Anal. Appl.**194**(1995), 823--844*Thirty years after Sharkovskii's Theorem*, Internat. J. Bifur. Chaos Appl. Sci. Engrg.**5**(1995), 1275--1281*Continuity of entropy revisited*, in "Dynamical Systems and Applications" (World Scientific Series in Applicable Analysis, vol. 4), World Scientific, Singapore, 1995, pp. 495--503*Lacing irregular shoes*, Math. Inteligencer**18**No. 4 (1996), 32--34*Entropy of transitive tree maps*(with Ll. Alseda, S. Baldwin and J. Llibre), Topology**36**(1997), 519--532*Trajectory of the turning point is dense for almost all tent maps*(with K. Brucks), Ergod. Th. & Dynam. Sys.**16**(1996), 1173--1183*New order for periodic orbits of interval maps*(with A. Blokh), Ergod. Th. & Dynam. Sys.**17**(1997), 565--574*Dense set of negative Schwarzian maps whose critical points have minimal limit sets*(with A. Blokh), Discrete Contin. Dynam. Sys.**4**(1997), 141--158*Entropy and over-rotation numbers for interval maps*(with A. Blokh), Proc. Steklov Inst. Math.**216**(1997), 229--235*Remarks on Sharkovsky's Theorem*, Amer. Math. Monthly**104**(1997), 846--847*Shear rotation numbers*(with E. Doeff), Nonlinearity**10**(1997), 1755--1762*Entropy of twist interval maps*(with A. Blokh), Isr. J. Math.**102**(1997), 61--100*Collet-Eckmann maps are unstable*(with A. Blokh), Commun. Math. Phys.**191**(1998), 61--70*Badly ordered cycles of circle maps*(with Ll. Alseda and J. Llibre), Pacific J. Math.**184**(1998), 23--41*Rotating an interval and a circle*(with A. Blokh), Trans. Amer. Math. Soc.**351**(1999), 63--78*Wild attractors of polymodal negative Schwarzian maps*(with A. Blokh), Commun. Math. Phys.**199**(1998), 397--416*Rotation and entropy*(with W. Geller), Trans. Amer. Math. Soc.**351**(1999), 2927--2948*Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval*(with S. Kolyada and L.Snoha), Fundam. Math.**160**(1999), 161--181*Low-dimensional Combinatorial Dynamics*(with Ll. Alseda and J. Llibre), Internat. J. Bifur. Chaos Appl. Sci. Engrg.**9**(1999), 1687--1704*Typical limit sets of critical points for smooth interval maps*(with A. Blokh), Ergod. Th. & Dynam. Sys.**20**(2000), 15--45*Topological entropy for multidimensional perturbations of one-dimensional maps*(with P. Zgliczynski), Internat. J. Bifur. Chaos Appl. Sci. Engrg.**11**(2001), 1443--1446*Rotation numbers for certain maps of an n-od*(with A. Blokh), Topol. Appl.**114**(2001), 27--48*Combinatorial Dynamics*, Topology Atlas Invited Contributions**6**(2001), 1--3*Attractors for graph critical rational maps*(with A. Blokh), Trans. Amer. Math. Soc.**354**(2002), 3639--3661*Possible jumps of entropy for interval maps*, Qualit. Th. Dyn. Sys.**2**(2001), 289--306*Topological Methods in Dynamics*(with J. Franks), in "Handbook of Dynamical Systems", vol. 1A, eds. B. Hasselblatt and A. Katok, Elsevier, Amsterdam 2002, pp. 547--598*Permutations and topological entropy for interval maps*, Nonlinearity**16**(2003), 971--976*Linear orderings and the sets of periods for star maps*(with Ll. Alseda), J. Math. Anal. Appl.**285**(2003), 50--61*On Bowen's definition of topological entropy*, Discrete Contin. Dyn. Syst., Ser. A,**10**(2004), 827--833*Topological entropy*, in "Encyclopedia of General Topology", eds. K. P. Hart, J. Nagata and J. E. Vaughan, Elsevier, Amsterdam 2003, pp. 147--149*Entropy of maps with horizontal gaps*, Internat. J. Bifur. Chaos Appl. Sci. Engrg.**14**(2004), 1489--1492*Expanding polymodials*(with A. Blokh and C. Cleveland), in "Modern Dynamical Systems and Applications", eds. M. Brin, B. Hasselblatt and Ya. Pesin, Cambridge University Press, Cambridge, 2004, pp. 253--270*Real 3x+1*(with A. Rodrigues), Proc. Amer. Math. Soc.**133**(2005), 1109--1118 ( posted electronically on October 15, 2004)*Branched derivatives*(with A. Blokh), Nonlinearity**18**(2005), 703--715 ( posted electronically on December 13, 2004)*Attractors and recurrence for dendrite-critical polynomials*(with A. Blokh), J. Math. Anal. Appl.**306**(2005), 567--588*Strict inequalities for the entropy of transitive piecewise monotone maps*(with P. Raith), Discrete Contin. Dynam. Sys.**13**(2005), 451--468*Ergodic natural measures*, in "Algebraic and Topological Dynamics" (Contemporary Mathematics**385**), eds. S. Kolyada, Y. Manin and T. Ward, Amer. Math. Soc., Providence, RI (2005), pp. 1--6*Irrational Life*(with W. Geller), Experimental Math.**14**(2005), 271--275*Iterations of linear maps over finite fields*(with J. G. Stevens and D. M. Thomas), Linear Algebra Appl.**413**(2006), 218--234 (posted electronically on October 25, 2005)*Julia sets of expanding polymodials*(with A. Blokh and C. Cleveland), Ergod. Th. & Dynam. Sys.**25**(2005), 1691--1718 (posted electronically on November 16, 2005)*Negative periodic orbits for graph maps*(with J. Llibre), Nonlinearity**19**(2006), 741-746 (posted electronically on February 6, 2006)*A Strong Hot Spot Theorem*(with D. H. Bailey), Proc. Amer. Math. Soc.**134**(2006), 2495-2501 ( posted electronically on March 22, 2006)*Strange Adding Machines*(with L. Block and J. Keesling), Ergod. Th. & Dynam. Sys.**26**(2006), 673-682 ( posted electronically on March 24, 2006)*Rotation sets of billiards with one obstacle*(with A. Blokh and N. Simanyi), Commun. Math. Phys.**266**(2006), 239-265 ( posted electronically on April 14, 2006)*Exact Devaney chaos and entropy*(with D. Kwietniak), Qualit. Th. Dyn. Sys.**6**(2005), 169-179*Affine actions of a free semigroup on the real line*(with V. Bergelson and S. Senti), Ergod. Th. & Dynam. Sys.**26**(2006), 1285 - 1305*Double standard maps*(with A. Rodrigues), Commun. Math. Phys.**273**(2007), 37-65 ( posted electronically on March 13, 2007)*Dynamics of the Nash map in the game of Matching Pennies*(with R. A. Becker, S. K. Chakrabarti, W. Geller and B. Kitchens), J. Difference Equ. Appl.**13**(2007), 223-235-
*Planar finitely Suslinian compacta*(with A. Blokh and L. Oversteegen), Proc. Amer. Math.Soc.**135**(2007), 3755-3764 (posted electronically on August 15, 2007) *Combinatorial Dynamics*, Scholarpedia, 2(10):3228 (2007)*Rotation Theory*, Scholarpedia, 2(10):3873 (2007)*Topological entropy*(with R. Adler and T. Downarowicz), Scholarpedia, 3(2):2200 (2008)-
*On the tip of the tongue*(with A. Rodrigues), J. Fixed Point Theory Appl.**3**(2008), 131-141 (posted electronically on April 1, 2008) -
*Real saddle-node bifurcation from a complex viewpoint*(with R. A. Perez), Conform. Geom. Dyn.**12**(2008), 97-108 -
*Attractors for unimodal quasiperiodically forced maps*(with Ll. Alseda), J. Difference Equ. Appl.**14**(2008), 1175-1196 -
*Sets of constant distance from a compact set in 2-manifolds with a geodesic metric*(with A. Blokh and L. Oversteegen), Proc. Amer. Math. Soc.**137**(2009), 733-743 (posted electronically on October 8, 2008) -
*Local critical perturbations of unimodal maps*(with A. Blokh), Commun. Math. Phys.**289**(2009), 765-776 (posted electronically on January 13, 2009) -
*Omega-limit sets for spiral maps*(with B. Kitchens), Discrete Contin. Dynam. Sys.**27**(2010), 787 - 798 (posted electronically on February 25, 2010) *Omega-limit sets for the Stein-Ulam Spiral map*(with K. Baranski), Topology Proceedings**36**(2010), 145 - 172 (posted electronically on March 2, 2010)-
*Microdynamics for Nash maps*(with W. Geller and B. Kitchens), Discrete Contin. Dynam. Sys.**27**(2010), 1007 - 1024 (posted electronically on March 31, 2010) *Euler approximations can destroy unbounded solutions*(with R. T. Guy), Fasciculi Mathematici**44**(2010), 43 - 52*Sensitive dependence on parameters*, J. Math. Phys.**51**(2010), 102704 (12 pages) (posted electronically on October 22, 2010)-
*A note on a rational difference equation*(with Ll. Alseda), J. Difference Equ. Appl.**17**(2011), 1711 - 1713 (posted electronically on February 23, 2011) -
*Non-generic cusps*(with A. Rodrigues), Trans. Amer. Math. Soc.**363**(2011), 3553 - 3572 (posted electronically on February 18, 2011) -
*Singular limits of absolutely continuous invariant measures for families of transitive maps*(with P. Eslami), J. Difference Equ. Appl.**18**(2011), 739 - 750 (posted electronically on July 4, 2011) -
*Hyperbolic dynamics in Nash maps*(with R. A. Becker, S. K. Chakrabarti, W. Geller and B. Kitchens), in: Discrete Dynamics and Difference Equations (Proceedings of the Twelfth International Conference on Difference Equations and Applications), World Scientific, Singapore 2010, pp. 15 - 45 -
*The dynamics of the Nash map for 2 by 2 games*(with R. A. Becker, S. K. Chakrabarti, W. Geller and B. Kitchens), in: Dynamics, Games and Science II, Springer Proceedings in Mathematics, 2011, Volume 2, pp. 549 - 565 -
*Fixed points for positive permutation braids*(with A. Rodrigues), Fund. Math.**216**(2012), 129 - 146 -
*A spectral radius estimate and entropy of hypercubes*(with W. Geller, B. Kitchens and M. Rams), J. Bifur. Chaos Appl. Sci. Engrg.**22**(2012), 1250096 (6 pages) *Irrational square roots*, College Math. J.**44**(2013), 53 - 55-
*Turning numbers for periodic orbits of disk homeomorphisms*(with A. Rodrigues), J. Fixed Point Th. Appl.**13**(2013), 241 - 258 (posted electronically on April 26, 2013) -
*Spectral radius of a nonnegative matrix: from Rome to Indy*, Proc. Amer. Math. Soc.**141**(2013), 3977 - 3983 (posted electronically on July 30, 2013) *Random interval homeomorphisms*(with Ll. Alseda), Proceedings of*New Trends in Dynamical Systems*. Salou, 2012, Publ. Mat. (2014), 15 - 36-
*Spaces of transitive interval maps*(with S. Kolyada and L. Snoha), Ergod. Th. & Dynam. Sys.**35**(2015), 2151 - 2170 (posted electronically on August 5, 2014) -
*Skew Product Attractors and concavity*(with Ll. Alseda), Proc. Amer. Math. Soc.**143**(2015), 703 - 716 (posted electronically on October 3, 2014) -
*Periodic points of latitudinal sphere maps*, J. Fixed Point Th. Appl.**16**(2014) 149 - 158 (posted electronically on November 5, 2014) -
*No semiconjugacy to a map of constant slope*(with S. Roth), Ergod. Th. & Dynam. Sys.**36**(2016), 875 - 889 (posted electronically on November 10, 2014) -
*Semiconjugacy to a map of a constant slope*(with Ll. Alseda), Discrete Contin. Dynam. Sys. B**20**(2015), 3403 - 3413 (posted electronically on September 30, 2015) *Loops of transitive interval maps*(with S. Kolyada and L. Snoha), in: Dynamics and Numbers, Contemporary Math.**669**, Amer. Math. Soc., Providence, RI, 2016, pp. 137 - 154-
*Symbolic dynamics for Lozi maps*(with S. Stimac), Nonlinearity**29**(2016), 3031 - 3046 (posted electronically on August 19, 2016) -
*Periodic points of latitudinal maps of the m-dimensional sphere*(with G. Graff and P. Nowak-Przygodzki), Discrete Contin. Dynam. Sys. A**36**(2016), 6187 - 6199 (posted electronically on August 31, 2016) -
*Counting preimages*(with A. Rodrigues), Ergod. Th. & Dynam. Sys. (posted electronically on January 24, 2017) -
*Constant slope maps on the extended real line*(with S. Roth), Ergod. Th. & Dynam. Sys. (posted electronically on May 2, 2017) *Entropy locking*(with D. Cosper) Fund. Math.**241**(2018), 83 - 96 (posted electronically on September 25, 2017)*Farey-Lorenz permutations for interval maps*(with W. Geller), Internat. J. Bifur. Chaos Appl. Sci. Engrg.**28**(2018), 1850021 [7 pages]*Shub's conjecture for smooth longitudinal maps of S*(with G. Graff and P. Nowak-Przygodzki), J. Difference Equ. Appl. (posted electronically on March 25, 2018)^{m}*Lozi-like maps*(with S. Stimac), Discrete Contin. Dynam. Sys. A**38**(2018), 3003 - 3023

*Periodic points for sphere maps preserving monopole foliations*(with G. Graff and P. Nowak-Przygodzki): abstract, PDF file*A fresh look at the notion of normality*(with V. Bergelson and T. Downarowicz): abstract, PDF file

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Last updated: May 11, 2018