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Differentiable and Complex Dynamics of Several Variables : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Pei-Chu Hu

Differentiable and Complex Dynamics of Several Variables

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

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Published: 31st July 1999
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The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.

Preface
Fatou-Julia type theoryp. 1
Ergodic theorems and invariant setsp. 39
Hyperbolicity in differentiable dynamicsp. 63
Some topics in dynamicsp. 99
Hyperbolicity in complex dynamicsp. 137
Iteration theory on P[superscript m]p. 179
Complex dynamics in C[superscript m]p. 203
Foundations of differentiable dynamicsp. 233
Foundations of complex dynamicsp. 275
Bibliographyp. 319
Indexp. 335
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792357711
ISBN-10: 079235771X
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 342
Published: 31st July 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 3.18
Weight (kg): 0.68