Nonlinear Dynamics and Chaotic Phenomena

Name: Nonlinear Dynamics and Chaotic Phenomena
Brand: Springer
SKU: 9789048149261
Price: 105.02 EUR
Availability: InStock

An Introduction

Автор: B.K Shivamoggi

Език:

Корици: С меки корици

Издател: Springer

Наличност: Външен склад

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FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasi...

Информация за книгата

Автор

B.K Shivamoggi

Език

Английски език

Корици

Книга - С меки корици

Издадена

2011

страници

410

EAN

9789048149261

ISBN

9048149266

Enbook ID

05322436

Издател

Springer

Теглоt

678

Размери

155 x 235 x 24

Пълно описание

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

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Nonlinear Dynamics and Chaotic Phenomena

An Introduction

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