منابع مشابه
Genericity 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...
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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...
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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.
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in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولRemoving 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-...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2002
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385702001165