Open problems in symbolic dynamics
Mike Boyle · Contemporary mathematics - American Mathematical Society · 2008
Equivalence Conjecture 4. Range of the dimension representation 5. Positive Rational Shift Equivalence Conjecture 6.The Generalized Spectral Conjecture 7. The Equal Entropy Factors Conjecture for SFTs 8.The factors problem for sofic shifts 9.The Good Finitary Conjecture for Markov shifts 10.What can be a beta function?11.Structure of expansive subdynamics 12. Can nonSFT expansive maps commute with irreducible SFTs? 13.The Commuting Powers Conjecture for SFTs 14. Jointly invariant measures 15.Z d SFTs 16.Stable limit sets of cellular automata 17.Algebraic Z d SFTs 18. Finitary codes and Markov random fields 19.Decidability problems 20.Onesided SFTs: the embedding problem 21.Onesided sofic shifts: the classification problem 22.The Virtual FOG Conjecture for automorphisms of a mixing SFT 23.Topological orbit equivalence 24.Symbolic extension entropy and entropy structure 25.Cellular automata and periodic points 26.Cellular automata on big groups 27.Entropy conjugacy and countable state Markov chains 28.Beta shifts: Salem numbers and intrinsic ergodicity 29.Adler's Renewal Question 30.The Road Coloring Problem 31.Parry's Finiteness Question for skew products 32.Classification of sofic shifts 33.Classification and flow equivalence of general shifts 34.The Pisot Conjecture 35.Nivat's Conjecture