Introduction to Non-uniform and Partial Hyperbolicity
نویسنده
چکیده
These are notes for a minicourse given at Regional Norte UdelaR in Salto, Uruguay for the conference “CIMPA Research School Hamiltonian and Langrangian Dynamics”. They are a preliminary version which have not had enough proof-reading, in particular there can be errors of any type (orthographical, typos, and mainly serious mistakes). Any comment is welcome. The purpose of the notes is to present the theory of non-uniformly hyperbolic diffeomorphisms trying to concentrate in some simplified contexts and explain some of the main techniques in the field. Some of the topics include: Lyapunov exponents, Invariant manifolds (Pesin theory and persistence properties) and dynamical consequences. The topics will help introduce some concepts for the second part of the minicourse given by M.C. Arnaud but will also cover some topics of independent interest.
منابع مشابه
New Criteria for Ergodicity and Non-uniform Hyperbolicity
In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this criterion in combination with topological devices such as blenders lets us obtain global ergodicity and abundance of non-zero Lyapunov exponents in some context...
متن کاملShadowing by Non Uniformly Hyperbolic Periodic Points and Uniform Hyperbolicity
We prove that, under a mild condition on the hyperbolicity of its periodic points, a map g which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map). In particular, this result gives a partial positive answer for a question done by A. Katok, in a related context.
متن کاملPesin Theory
Pesin Theory-An important branch of dynamical systems and of smooth ergodic theory, with many applications to non-linear dynamics. The name is due to the landmark work of Yakov B. Pesin in the mid-seventies 20, 21, 22]. Sometimes it is also referred to as the theory of smooth dynamical systems with non-uniformly hyperbolic behavior, or simply theory of non-uniformly hyperbolic dynamical systems...
متن کاملPesin Theory
Pesin Theory-An important branch of dynamical systems and of smooth ergodic theory, with many applications to non-linear dynamics. The name is due to the landmark work of Yakov B. Pesin in the mid-seventies 20, 21, 22]. Sometimes it is also referred to as the theory of smooth dynamical systems with non-uniformly hyperbolic behavior, or simply theory of non-uniformly hyperbolic dynamical systems...
متن کاملCOCYCLES OVER PARTIALLY HYPERBOLIC MAPS par
A diffeomorphism f : M → M on a compact manifold M is partially hyperbolic if there exists a continuous, nontrivial Df -invariant splitting TxM = E s x ⊕ E c x ⊕ E u x , x ∈ M of the tangent bundle such that the derivative is a contraction along E and an expansion along E, with uniform rates, and the behavior of Df along the center bundle E is in between its behaviors along E and E, again by a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015