Differentiable and Complex Dynamics of Several Variables: 483 (Mathematics and Its Applications) - Softcover

Pei-Chu Hu, Pei-Chu; Chung-Chun Yang

Softcover

ISBN 10: 9048152461 ISBN 13: 9789048152469

Verlag: Springer, 2010

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Reseña del editor

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.

Reseña del editor

This book gives a comprehensive and up-to-date survey on dynamics and related topics, such as Fatou-Julia type theory, the Ergodic theorem and invariant sets, hyperbolicity in differentiable or complex dynamics, iterant ion theory on Pm, complex dynamics in Cm and the foundations of differentiable and complex dynamics. The main aims of this volume are, firstly, to advance the study of the above-named topics and to establish the corresponding Fatou-Julia results for complex manifolds, and, secondly, to provide some advanced account of dynamical systems within the framework of geometry and analysis, presented from a unified approach applicable to both real and complex manifolds.
Audience: This work will be of interest to graduate students and researchers involved in the fields of global analysis, analysis on manifolds, several complex variables and analytic spaces, partial differential equations, differential geometry, measure and integration.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• ISBN 10: 9048152461
• ISBN 13: 9789048152469
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 352