منابع مشابه
Removing zero Lyapunov exponents in volume-preserving flows
Baraviera and Bonatti in [1] proved that it is possible to perturb, in the Ctopology, a volume-preserving and partial hyperbolic diffeomorphism in order to obtain a non-zero sum of all the Lyapunov exponents in the central direction. In this article we obtain the analogous result for volume-preserving flows. MSC 2000: primary 37D30, 37D25; secondary 37A99. keywords: Dominated splitting; volume-...
متن کاملGenericity of Zero Lyapunov Exponents
We show that, for any compact surface, there is a residual (dense Gδ) set of C 1 area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mañé, but no proof was available. We also show that for any fixed ergodic dynamical system over a compact space, there is a residual set of continuous SL(2, R)-cocycles which either are unifo...
متن کاملNon - Zero Lyapunov Exponents and Axiom
Let f : M → M be a C 1 diffeomorphism of a compact manifold M admitting a dominated splitting T M = E cs ⊕ E cu. We show that if the Lyapunov exponents of f are nonzero and have the same sign along the E cs and E cu directions on a total probability set (a set with probability one with respect to every f-invariant measure), then f is Axiom A. We also show that a f-ergodic measure whose Lyapunov...
متن کاملOn Essential Coexistence of Zero and Nonzero Lyapunov Exponents
We show that there exists a C∞ volume preserving diffeomorphism P of a compact smooth Riemannian manifold M of dimension 4, which is close to the identity map and has nonzero Lyapunov exponents on an open and dense subset G of not full measure and has zero Lyapunov exponent on the complement of G. Moreover, P |G has countably many disjoint open ergodic components.
متن کاملSymplectic Diffeomorphisms: Partial Hyperbolicity and Zero Center Lyapunov Exponents
It is proven that for a C-generic symplectic diffeomorphism f of any closed manifold, the Oseledets splitting along almost every orbit is either trivial or partially hyperbolic. In addition, if f is not Anosov then all the exponents in the center bundle vanish. This establishes in full a result announced by Mañé in the ICM 1983. The main technical novelty is a probabilistic method for the const...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2003
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385702001773