Fast growth of the number of periodic points arising from heterodimensional connections

DOI10.1112/S0010437X21007405zbMath1479.37029arXiv1808.07218OpenAlexW3191742077MaRDI QIDQ5009393

Masayuki Asaoka, Katsutoshi Shinohara, Dmitry V. Turaev

Publication date: 23 August 2021

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.07218

zbMATH Keywords

blendersgrowth of periodic pointspartially hyperbolic diffeomorphismsheterodimensional cycles

Mathematics Subject Classification ID

Orbit growth in dynamical systems (37C35) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (2)

Almost blenders and parablenders ⋮ On super-exponential divergence of periodic points for partially hyperbolic systems

Cites Work

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• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• Super exponential growth of the number of periodic orbits inside homoclinic classes
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Julia-Fatou-Sullivan theory for real one-dimensional dynamics
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Generic diffeomorphisms with superexponential growth of number of periodic orbits
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Persistent nonhyperbolic transitive diffeomorphisms
• An extension of the Artin-Mazur theorem
• Pathological foliations and removable zero exponents
• Maps close to identity and universal maps in the Newhouse domain
• On periodic points
• Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics
• Partially hyperbolic fixed points
• Nonremovable zero Lyapunov exponent
• Robust criterion for the existence of nonhyperbolic ergodic measures
• Abundance of $C^{1}$-robust homoclinic tangencies
• A C^r unimodal map with an arbitrary fast growth of the number of periodic points
• Local Contractions and a Theorem of Poincare
• Periodic points and homoclinic classes
• On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I
• ROBUST HETERODIMENSIONAL CYCLES AND $C^1$-GENERIC DYNAMICS
• Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes
• ON DIMENSION OF NON-LOCAL BIFURCATIONAL PROBLEMS
• MINIMALITY OF STRONG STABLE AND UNSTABLE FOLIATIONS FOR PARTIALLY HYPERBOLIC DIFFEOMORPHISMS
• Heterodimensional cycles, partial hyperbolicity and limit dynamics
• Growth of number of periodic orbits of one family of skew product maps
• Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations
• Blenders in centre unstable Hénon-like families: with an application to heterodimensional bifurcations
• Invariant manifolds
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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