Ergodic and chaotic properties of Lipschitz maps on smooth surfaces
نویسندگان
چکیده
We construct noninvertible maps on every compact surface and study their chaotic properties from both the measure theoretic and topological points of view. We use some topological techniques employed by others for diffeomorphisms and extend to the noninvertible case.
منابع مشابه
Chaotic Dynamics in Hybrid Systems
In this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological dynamics and ergodic theory may be used to study hybrid systems, and review existing bifurcation theory for one-...
متن کاملWatermarking Scheme Based on Multiple Chaotic Maps
a watermarking scheme for Grayscale image isproposed based on a family of the chaotic maps and discretecosine transform. Jacobian Elliptic mapis employed to encrypt ofwatermarked logo. Piecewise nonlinear chaotic map is also usedto determine the location of DCT coefficients for the watermarkembedding. The purpose of this algorithm is to improve theshortcoming of watermarking such as small key s...
متن کاملIntrinsic Ergodicity of Fibered Perturbations of Products of Chaotic Smooth Interval Maps
We consider small bered perturbations of direct products of chaotic smooth interval maps. We prove that these multi-dimensional systems have a non-zero and nite number of invariant and ergodic probability measures with maximal entropy. We note that these dynamical systems are neither linear nor expansive. The proof uses a suitable generalization of Hofbauer's Markov diagram developped in 6] whi...
متن کاملChaotic Sequences of I.I.D. Binary Random Variables with Their Applications to Communications
The Bernoulli shift is a fundamental theoretic model of a sequence of independent and identically distributed(i.i.d.) binary random variables in probability theory, ergodic theory, information theory, and so on. We give a simple sufficient condition for a class of ergodic maps with some symmetric properties to produce a chaotic sequence of i.i.d. binary random variables. This condition is expre...
متن کاملLectures on Lyapunov Exponents and Smooth Ergodic Theory
1. Lyapunov Exponents for Differential Equations 2. Abstract Theory of Lyapunov Exponents 3. Regularity of Lyapunov Exponents Associated with Differential Equations 4. Lyapunov Stability Theory 5. The Oseledets Decomposition 6. Dynamical Systems with Nonzero Lyapunov Exponents. Multiplicative Ergodic Theorem 7. Nonuniform Hyperbolicity. Regular Sets 8. Examples of Nonuniformly Hyperbolic System...
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 2012