Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics

DOI10.1007/s00208-016-1468-0zbMath1384.37028arXiv1506.07279OpenAlexW2203439608MaRDI QIDQ2402843

Masayuki Asaoka, Katsutoshi Shinohara, Dmitry V. Turaev

Publication date: 15 September 2017

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.07279

zbMATH Keywords

attractorrepellersemigroup actionuniversal dynamics

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Orbit growth in dynamical systems (37C35) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems involving maps of the interval (37E05) Periodic and quasi-periodic flows and diffeomorphisms (37C55) General theory of random and stochastic dynamical systems (37H05)

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Abundance of fast growth of the number of periodic points in two-dimensional area-preserving dynamics ⋮ Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors ⋮ On super-exponential divergence of periodic points for partially hyperbolic systems ⋮ Fast growth of the number of periodic points arising from heterodimensional connections

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