Historic behavior in nonhyperbolic homoclinic classes
Copyright policy )Historic behavior in nonhyperbolic homoclinic classes
We show that C 1 C^1 -generically for diffeomorphisms of manifolds of dimension d ≥ 3 d\geq 3 , a homoclinic class containing saddles of different indices has a residual subset where the orbit of any point has historic behavior.
- Tokyo Metropolitan University Japan
- Tokai University Japan
Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Dynamical systems with hyperbolic orbits and sets, homoclinic class, Dynamical systems involving smooth mappings and diffeomorphisms, FOS: Mathematics, Homoclinic and heteroclinic orbits for dynamical systems, Attractors and repellers of smooth dynamical systems and their topological structure, diffeomorphisms of manifolds, Dynamical Systems (math.DS), Generic properties, structural stability of dynamical systems, Mathematics - Dynamical Systems
Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Dynamical systems with hyperbolic orbits and sets, homoclinic class, Dynamical systems involving smooth mappings and diffeomorphisms, FOS: Mathematics, Homoclinic and heteroclinic orbits for dynamical systems, Attractors and repellers of smooth dynamical systems and their topological structure, diffeomorphisms of manifolds, Dynamical Systems (math.DS), Generic properties, structural stability of dynamical systems, Mathematics - Dynamical Systems
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