“Quadratic Map”的概念、定义、习题解题方法及翻译-数学辞典

单词

Quadratic Map

释义

Quadratic Map

A 1-D Map often called ``the'' quadratic map is defined by

(1)

This is the real version of the complex map defining the Mandelbrot Set. The quadratic map is called attracting if theJacobian

, and repelling if

. Fixed Points occur when

(2)

(3)

(4)

Period two Fixed Points occur when


			(5)

(6)

(7)

Period three Fixed Points occur when


	(8)

The most general second-order 2-D Map with an elliptic fixed point at the origin has the form

			(9)
			(10)

The map must have a Determinant of 1 in order to be Area preserving, reducing the number of independent parameters from seven to three. The map can then be put in a standard form by scaling and rotating to obtain

			(11)
			(12)

The inverse map is

			(13)
			(14)

The Fixed Points are given by

(15)

for

, ...,

See also Bogdanov Map, Hénon Map, Logistic Map, Lozi Map, Mandelbrot Set

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。