Geometric and Probabilistic Structures in Dynamics.
Burns, Keith.
Geometric and Probabilistic Structures in Dynamics. - 1st ed. - 1 online resource (358 pages) - Contemporary Mathematics ; v.469 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- Nonconvergence examples in averaging -- Periodic rank one geodesics in Hadamard spaces -- Dynamical determinants and spectrum for hyperbolic diffeomorphisms -- Open problems in symbolic dynamics -- 1. Introduction -- 2. Definitions -- 3. Classification of SFTs and the Little Shift 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. Zd SFTs -- 16. Stable limit sets of cellular automata -- 17. Algebraic Zd 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 -- Appendices -- Appendix A. Commuting SFTs and periodic points -- Appendix B. Commuting SFTs from commuting matrices, following Nasu. Appendix C. LR Textile Systems -- Appendix D. Commuting SFTs from matrices commuting on dimension -- Appendix E. Primitive matrices SE but not SSE over Z+ [1/p] -- Appendix F. Examples for the onesided sofic classification problem -- Bibliography -- New examples of topologically equivalent S-unimodal maps with different metric properties -- Appendix. Quasiconformal deformation of multipliers -- A remark on the group of PL-homeomorphisms in dimension one -- Fermi acceleration -- Introduction -- Stochastic models -- One and a half degree of freedom -- Several degrees of freedom -- Galton board -- Conclusions -- References -- Riemannian 2-step nilmanifolds with prescribed Ricci tensor -- On the Greenfield-Wallach and Katok conjectures in dimension three -- Metastability and Stochastic Resonance for Multiscale Systems -- Mendelian Dynamics and Sturtevant's Paradigm -- On the estimation of topological entropy on surfaces -- 1. Introduction -- 2. Definition and properties of Topological Entropy -- 3. Trellises and Entropy -- 4. Computing stable and unstable manifolds -- 5. Computation of the stable and unstable manifolds in Henon Maps -- 6. Rigorous Topological Arguments in the Plane with Taylor Models -- 7. An alternate numerical description of the rectangles Ri and their properties -- References -- Dynamical Systems and Differential Forms. Low Dimensional Hamiltonian Systems -- Periodic orbits and holonomy for hyperbolic flows -- On existence and uniqueness of weak foliations in dimension 3 -- A Limit Theorem for Birkhoff sums of non-integrable functions over rotations.
9780821881484
Differentiable dynamical systems -- Congresses.
Geometry, Algebraic -- Congresses.
Electronic books.
QA614.8 -- .W675 2008eb
515/.39
Geometric and Probabilistic Structures in Dynamics. - 1st ed. - 1 online resource (358 pages) - Contemporary Mathematics ; v.469 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- Nonconvergence examples in averaging -- Periodic rank one geodesics in Hadamard spaces -- Dynamical determinants and spectrum for hyperbolic diffeomorphisms -- Open problems in symbolic dynamics -- 1. Introduction -- 2. Definitions -- 3. Classification of SFTs and the Little Shift 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. Zd SFTs -- 16. Stable limit sets of cellular automata -- 17. Algebraic Zd 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 -- Appendices -- Appendix A. Commuting SFTs and periodic points -- Appendix B. Commuting SFTs from commuting matrices, following Nasu. Appendix C. LR Textile Systems -- Appendix D. Commuting SFTs from matrices commuting on dimension -- Appendix E. Primitive matrices SE but not SSE over Z+ [1/p] -- Appendix F. Examples for the onesided sofic classification problem -- Bibliography -- New examples of topologically equivalent S-unimodal maps with different metric properties -- Appendix. Quasiconformal deformation of multipliers -- A remark on the group of PL-homeomorphisms in dimension one -- Fermi acceleration -- Introduction -- Stochastic models -- One and a half degree of freedom -- Several degrees of freedom -- Galton board -- Conclusions -- References -- Riemannian 2-step nilmanifolds with prescribed Ricci tensor -- On the Greenfield-Wallach and Katok conjectures in dimension three -- Metastability and Stochastic Resonance for Multiscale Systems -- Mendelian Dynamics and Sturtevant's Paradigm -- On the estimation of topological entropy on surfaces -- 1. Introduction -- 2. Definition and properties of Topological Entropy -- 3. Trellises and Entropy -- 4. Computing stable and unstable manifolds -- 5. Computation of the stable and unstable manifolds in Henon Maps -- 6. Rigorous Topological Arguments in the Plane with Taylor Models -- 7. An alternate numerical description of the rectangles Ri and their properties -- References -- Dynamical Systems and Differential Forms. Low Dimensional Hamiltonian Systems -- Periodic orbits and holonomy for hyperbolic flows -- On existence and uniqueness of weak foliations in dimension 3 -- A Limit Theorem for Birkhoff sums of non-integrable functions over rotations.
9780821881484
Differentiable dynamical systems -- Congresses.
Geometry, Algebraic -- Congresses.
Electronic books.
QA614.8 -- .W675 2008eb
515/.39