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Open Problems in DS & ET (IUPUI, Indianapolis)

Open Problems in DS & ET (Institute of Mathematics, Kiev)

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 (Chairman - Benjamin Weiss). New problems are being added to it.

 If you would like to submit some open problems to this page, please send them to me 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). I would also appreciate any notification of open problems in "DS & ET" web links (some of them you can find also here).

  Anyone who has never had any (open) problem has never tried anything new. Anyone who has published a paper has solved a problem and maybe has some other open problems. Why not to present them at this www page? :-)

Sergiy Kolyada 

Geometric Models of Pisot Substitutions and Non-Commutative Arithmetic

Submitted by Pierre Arnoux Corrections - 29.11.2001

Ergodic Ramsey Theory - an  Update

Submitted by Vitaly Bergelson    ( See also:   http://www.math.ohio-state.edu/~vitaly/ )


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 - 21.10.2002

Entropy, Periodic Points and Transitivity of Maps

Submitted by Sergiy Kolyada   &  Lubomir Snoha Corrections - 26.10.2002

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   &  Serge Troubetzkoy


Is Any Kind of Mixing Possible in "ToP" N-actions?

Submitted by Tomasz Downarowicz   &  Xiangdong Ye       ( See also:    hefei.dvi)


Six Problems in Algebraic Dynamics

Submitted by Thomas Ward                  Corrections - 06.02.2007


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   &  Sergiy Kolyada       Corrections - 06.02.2007


The Law of Series

Submitted by Tomasz Downarowicz   &  Yves Lacroix


Problems on billiards, flat surfaces and translation surfaces

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


Open problems in dynamics and related fields

Submitted by Alexander Gorodnik

Last updated February 22, 2007Mail addressskolyada@imath.kiev.ua  

Open Problems Links

Michael Herman - Some Open Problems in Dynamical Systems

Open Problems in Dynamical Systems - SUNY at Stony Brook

Jérôme Buzzi - Questions

Problems in Low-Dimensional Topology (Rob Kirby)

3X+1 Problem and Related Problems


Some Open Problems -  Chapter 12 of the Book

Introduction to Finite Automata and Substitution Dynamical Systems

If you have some useful remarks or for any reason you want your link/picture to be removed let me know.