Dynamical Systems and Geometric Mechanics
Dynamical Systems and Geometric Mechanics

Author: Jared Maruskin

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-08-21

Total Pages: 417

ISBN-13: 3110598035

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Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.

Early Days in Complex Dynamics
Early Days in Complex Dynamics

Author: Daniel S. Alexander

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 474

ISBN-13: 0821844644

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The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.

Analytical Mechanics
Analytical Mechanics

Author: Antonio Fasano

Publisher: Oxford University Press on Demand

Published: 2006-04-06

Total Pages: 788

ISBN-13: 0198508026

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Is the solar system stable? Is there a unifying 'economy' principle in mechanics? How can a pointmass be described as a 'wave'? This book offers students an understanding of the most relevant and far reaching results of the theory of Analytical Mechanics, including plenty of examples, exercises, and solved problems.