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Open Problems in DS and ET (Institute of Mathematics,

Open Problems in DS and ET (Institut de Mathematiques
de Luminy)

Open  Problems in  Dynamical Systems & Ergodic Theory

  Welcome!  This collection of Open Problems in Dynamical Systems & Ergodic Theory originated from the Katsiveli - 2000  Open Problems Session. New problems are being added to it.

 If you would like to submit some open problems to this page, please send them to Sergiy Kolyada in the form of TeX or LaTeX files. Please make sure that the introduction and references to your open problems are as complete as possible (simply because this is helpful to readers who attempt to solve them). We would also appreciate any notification of open problems in "DS & ET" web links (some of them you can find also here).

 If you have any remarks about this page, please write to Sergiy Kolyada or Michal Misiurewicz.


Geometric models of Pisot substitutions and non-commutative arithmetic

Submitted by Pierre Arnoux (updated November 29, 2001)


Ergodic Ramsey Theory - an update

Submitted by Vitaly Bergelson (see also here)


Dense periodic points in cellular automata

Submitted by Francois Blanchard


Non-discrete locally compact second countable groups

Submitted by Sergey Gefter


Martingale convergence and ergodic theorems

Submitted by Alexander Kachurovskii       The problem is closed (October 21, 2002)


Entropy, periodic points and transitivity of maps

Submitted by Sergiy Kolyada and Lubomir Snoha (updated October 26, 2002)


Natural spectral isomorphisms

Submitted by Jan Kwiatkowski


Density of periodic orbit measures for piecewise monotonic interval maps

Submitted by Peter Raith


Polygonal billiards: some open problems

Submitted by Pascal Hubert and Serge Troubetzkoy


Is any kind of mixing possible in "ToP" N-actions?

Submitted by Tomasz Downarowicz and Xiangdong Ye (see also here)


Six problems in Algebraic Dynamics

Submitted by Thomas Ward (updated February 6, 2007)


Problems on billiards

Submitted by Eugene Gutkin


Is entropy effectively computable?

Submitted by John Milnor


Discrete logistic map

Submitted by Michal Misiurewicz


Does minimal action by the group of measure preserving transformations imply the existence of a uniquely ergodic transformation for a measure on a Cantor set?

Submitted by Ethan Akin


For minimal systems does Li-Yorke sensitivity occur exactly for extensions of nontrivial weak mixing systems?

Submitted by Ethan Akin and Sergiy Kolyada (updated February 6, 2007)


The Law of Series

Submitted by Tomasz Downarowicz and Yves Lacroix


Problems on billiards, flat surfaces and translation surfaces

Submitted by Pascal Hubert, Howard Masur, Thomas Schmidt and Anton Zorich (see comments by Zorich)


Open problems in dynamics and related fields

Submitted by Alexander Gorodnik


Open problem session - Sde-Boker 2013

Submitted by Barak Weiss


Last updated March 14, 2013


Back to the home page of Michal Misiurewicz


Open Problems links

Michael Herman - Some Open Problems in Dynamical

Open Problems in Dynamical Systems - SUNY at Stony

Problems in Low-Dimensional Topology (Rob Kirby)

3x+1 problem and related problems


Finite Automata and Substitution Systems

Open problems: Chapter 12