Websional then the diffeomorphism is partially hyperbolic and from this we deduce that the diffeomorphism is transitive. Keywords: Dominated splitting, C1 generic dynamics, homoclinic classes. Mathematical subject classification:37D30, 37C20, 37C70. 1 Introduction It is a main problem in generic dynamics to understand the structure of homo- WebSome author assume in their definition of Anosov diffeomorphisms that the diffeo is transitive. In that case, connectedness of M implies mixing. Also it is known that any …
Persistent Nonhyperbolic Transitive Diffeomorphisms
WebDec 7, 2024 · It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). Here we discuss the converse question. Transitivity of … WebNov 15, 2024 · The present work concerns to provide some sufficient conditions for transitivity of Anosov diffeomorphism. Our main result is the following theorem. Theorem A. Let f: M → M be a C 2-Anosov diffeomorphism. If J f n (p) = 1, for any p ∈ P e r (f), such that f n (p) = p, then f is transitive and leaves an invariant C 1 volume form. hotsheild for mac
Expansive transitive sets for robust and generic …
WebYou can find a demonstration of this fact (if M is connected) in the book of Milnor - Topology from the differentiable viewpoint. It is the lemma of homogeneity. WebSep 19, 2008 · Third, we extend a theorem by Sigmund on hyperbolic basic sets: every isolated transitive set L of any C^1-generic diffeomorphism f exhibits many ergodic hyperbolic measures whose supports coincide with the whole set L. In addition, confirming a claim made by R. Mané in 1982, we show that hyperbolic measures whose Oseledets … WebIn mathematics, a Lie groupoid is a groupoid where the set of objects and the set of morphisms are both manifolds, all the category operations (source and target, composition, identity-assigning map and inversion) are smooth, and the source and target operations ,: are submersions.. A Lie groupoid can thus be thought of as a "many-object … hotshells