Using Ulam's method to calculate entropy and other dynamical invariants
Using Ulam's method to calculate entropy and other dynamical invariants
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DOI：
10.1088/0951-7715/12/1/006
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发表时间：
1999-01-01
期刊：
影响因子：
1.7
通讯作者：
Froyland, G
中科院分区：
文献类型：
--
作者：
Froyland, G
利用Ulam方法的一种特殊形式，我们估计了三元组（M，T）的测度论熵。其中M是光滑流形，T是C1+y一致双曲映射，μ是T的唯一物理测度.通过一些额外的计算，我们还获得了（i）物理测度μ，（ii）T相对于Cc的李雅普诺夫指数，（iii）（T）的相关衰减率的数值估计。mu）相对于Cv测试功能，以及（iv）逃逸率（用于驱避剂）。考虑了四种主要情况：T处处扩张，T处处双曲（Anosov），T在吸引不变集上双曲（公理A吸引子），T在非吸引不变集上双曲（公理A非吸引子/排斥子）.
Using a special form of Ulam's method, we estimate the measure-theoretic entropy of a triple (M, T. mu), where M is a smooth manifold, T is a C1+y uniformly hyperbolic map, and mu is the unique physical measure of T. With a few additional calculations, we also obtain numerical estimates of(i) the physical measure mu, (ii) the Lyapunov exponents of T with respect to Cc, (iii) the rate of decay of correlations for (T. mu) with respect to Cv test functions, and (iv) the rate of escape (for repellors). Four main situations are considered: T is everywhere expanding, T is everywhere hyperbolic (Anosov), T is hyperbolic on an attracting invariant set (axiom A attractor], and T is hyperbolic on a non-attracting invariant set (axiom A non-attractor/repellor).