منابع مشابه
C-robust Transitivity for Surfaces with Boundary
We prove that C-robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are C−robustly transitive, with k ≥ 2. This class of diffeomorphisms are examples where a version of Palis’ conjecture on surfaces with boundary, about homoclinic tangencies and uniform hyperbolicity, does not hold in the C−topolog...
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One main task of smooth dynamical systems consists in finding a good decomposition into elementary pieces of the dynamics. This paper contributes to the study of chain-recurrence classes. It is known that Cgenerically, each chain-recurrence class containing a periodic orbit is equal to the homoclinic class of this orbit. Our result implies that in general this property is fragile. We build a C-...
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We prove that a divergence-free and C1-robustly transitive vector field has no singularities. Moreover, if the vector field is C4 then the linear Poincaré flow associated to it admits a dominated splitting over M . MSC 2000: primary 37D30, 37D25; secondary 37A99. keywords: Volume-preserving flows; Robust transitivity; Dominated splitting; Ergodicity.
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2012
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385712000247