Differentiable and Complex Dynamics of Several Variables

Pei-Chu Hu, Chung-Chun Yang (Autoren)

Buch | Softcover

342 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1999
Springer (Verlag)
978-90-481-5246-9 (ISBN)

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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.

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.

Erscheint lt. Verlag	5.12.2010
Reihe/Serie	Mathematics and Its Applications ; 483
Zusatzinfo	X, 342 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	90-481-5246-1 / 9048152461
ISBN-13	978-90-481-5246-9 / 9789048152469
Zustand	Neuware