Homoclinic points, atoral polynomials, and periodic points of algebraic -actions

DOI10.1017/S014338571200017XzbMath1294.37009arXiv1108.4989OpenAlexW2653723217MaRDI QIDQ2842227

Evgeny Verbitskiy, Klaus Schmidt, Douglas Lind

Publication date: 13 August 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.4989

zbMATH Keywords

growth of periodic pointsGelfond's estimatesummable homoclinic points

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Orbit growth in dynamical systems (37C35) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Topological entropy (37B40) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

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Representations of toral automorphisms ⋮ A survey of algebraic actions of the discrete Heisenberg group ⋮ Integrability and regularity of rational functions: ⋮ Combinatorial independence and sofic entropy ⋮ Homoclinically expansive actions and a garden of Eden theorem for harmonic models ⋮ Singularities of rational inner functions in higher dimensions ⋮ New directions in algebraic dynamical systems ⋮ Divisor divisibility sequences on tori ⋮ Max-min theorems for weak containment, square summable homoclinic points, and completely positive entropy ⋮ Algebraic actions of the discrete Heisenberg group: expansiveness and homoclinic points ⋮ Mahler's work and algebraic dynamical systems ⋮ Tropical limits of decimated polynomials ⋮ Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group ⋮ Harmonic models and Bernoullicity ⋮ Entropy, determinants, and $L^2$-torsion

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