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Aperiodic chain recurrence classes of -generic diffeomorphisms
Christian Bonatti, Katsutoshi Shinohara
We consider the space of -diffeomorphims equipped with the -topology on a three dimensional closed manifold. It is known that there are open sets in which -generic d…
A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class
Christian Bonatti, Katsutoshi Shinohara
We give a -perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain r…
Robust heterodimensional cycles in two-parameter unfolding of homoclinic tangencies
Dongchen Li, Xiaolong Li, Katsutoshi Shinohara +1
We establish a necessary and sufficient condition for the birth of heterodimensional cycles from a generic homoclinic tangency to a hyperbolic periodic orbit. We prove for ($…
Super exponential divergence of periodic points for C^1-generic partially hyperbolic homoclinic classes
Xiaolong Li, Katsutoshi Shinohara
A diffeomorphism f is called super exponential divergent if for every r>1, the lower limit of #Per_n(f)/r^n diverges to infinity as n tends to infinity, where Per_n(f) is the set o…
Fast growth of the number of periodic points arising from heterodimensional connections
Masayuki Asaoka, Katsutoshi Shinohara, Dmitry Turaev
We consider C^r-diffeomorphisms of a compact smooth manifold having a pair of robust heterodimensional cycles where r is a positive integer or infinity. We prove that if certain co…
Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics
Masayuki Asaoka, Katsutoshi Shinohara, Dmitry Turaev
We consider semigroup actions on the unit interval generated by strictly increasing -maps. We assume that one of the generators has a pair of fixed points, one attracting and…