Differentiable and Complex Dynamics of Several Variables / Edition 1

by Pei-Chu Hu, Chung-Chun Yang

Overview

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.

Product Details

ISBN-13:	9780792357711
Publisher:	Springer Netherlands
Publication date:	07/31/1999
Series:	Mathematics and Its Applications , #483
Edition description:	1999
Pages:	342
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 Fatou-Julia type theory.- 2 Ergodic theorems and invariant sets.- 3 Hyperbolicity in differentiable dynamics.- 4 Some topics in dynamics.- 5 Hyperbolicity in complex dynamics.- 6 Iteration theory on—m.- 7 Complex dynamics in—m.- A Foundations of differentiable dynamics.- B Foundations of complex dynamics.