+612 9045 4394

CHECKOUT

# Differentiable and Complex Dynamics of Several Variables

### MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover Published: 31st July 1999
ISBN: 9780792357711
Number Of Pages: 342

### Hardcover

RRP \$353.99
\$244.75
31%
OFF
Ships in 7 to 10 business days

## Other Available Editions(Hide)

• Paperback View Product Published: 5th December 2010
\$169.73

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 theory p. 1 Ergodic theorems and invariant sets p. 39 Hyperbolicity in differentiable dynamics p. 63 Some topics in dynamics p. 99 Hyperbolicity in complex dynamics p. 137 Iteration theory on P[superscript m] p. 179 Complex dynamics in C[superscript m] p. 203 Foundations of differentiable dynamics p. 233 Foundations of complex dynamics p. 275 Bibliography p. 319 Index p. 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