“Arnold's Cat Map”的概念、定义、习题解题方法及翻译-数学辞典

单词

Arnold's Cat Map

释义

Arnold's Cat Map

The best known example of an Anosov Diffeomorphism. It is given by the Transformation

(1)

where

and

are computed mod 1. The Arnold cat mapping is non-Hamiltonian, nonanalytic, and mixing. However, it is Area-Preserving since the Determinant is 1. The LyapunovCharacteristic Exponents are given by

(2)

(3)

The Eigenvectors are found by plugging

into the Matrix Equation

(4)

For

, the solution is

(5)

where

is the Golden Ratio, so the unstable (normalized) Eigenvector is

(6)

Similarly, for

, the solution is

(7)

so the stable (normalized) Eigenvector is

(8)

See also Anosov Map

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。