Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-019-09752-3
Abstract: In this paper, we prove that for $$C^1$$ C 1 -generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with $$j>i+1$$ j > i + 1 , and the homoclinic… read more here.
Keywords: ergodic measures; homoclinic class; multi zero; measures multi ... See more keywords
Hyperbolicity versus weak periodic orbits inside homoclinic classes
Sign Up to like & getrecommendations! Published in 2017 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2016.122
Abstract: We prove that, for $C^{1}$ -generic diffeomorphisms, if the periodic orbits contained in a homoclinic class $H(p)$ have all their Lyapunov exponents bounded away from zero, then $H(p)$ must be (uniformly) hyperbolic. This is in… read more here.
Keywords: weak periodic; inside homoclinic; homoclinic class; periodic orbits ... See more keywords