Super exponential growth of the number of periodic orbits inside homoclinic classes

zbMath1145.37015MaRDI QIDQ928450

Todd Fisher, Christian Bonatti, Lorenzo J. Dıaz

Publication date: 18 June 2008

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

homoclinic classheterodimensional cyclechain recurrence classArtin-Mazur diffeomorphismindex of a saddlesymbolic extensions

Mathematics Subject Classification ID

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 (8)

Extreme growth rate of periodic orbits for equivalent differentiable flows ⋮ Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics ⋮ Abundance of fast growth of the number of periodic points in two-dimensional area-preserving dynamics ⋮ Growth of number of periodic orbits of one family of skew product maps ⋮ Periodic points and measures for a class of skew-products ⋮ Smooth interval maps have symbolic extensions ⋮ On super-exponential divergence of periodic points for partially hyperbolic systems ⋮ Fast growth of the number of periodic points arising from heterodimensional connections

This page was built for publication: Super exponential growth of the number of periodic orbits inside homoclinic classes