
Differentiable and Complex Dynamics of Several Variables
Springer (Publisher)
Published on 5. December 2010
Book
Paperback/Softback
X, 342 pages
978-90-481-5246-9 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of hardcover 1st ed. 1999
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
X, 342 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 20 mm
Weight
534 gr
ISBN-13
978-90-481-5246-9 (9789048152469)
DOI
10.1007/978-94-015-9299-4
Schweitzer Classification
Other editions
Additional editions

Pei-Chu Hu | Chung-Chun Yang
Differentiable and Complex Dynamics of Several Variables
Book
07/1999
1st Edition
Kluwer Academic Publishers
€53.49
Shipment within 15-20 days
Content
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.