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Dynamical Systems and Geometric Mechanics: An Introduction
Hardcover
Series: de Gruyter Studies in Mathematical Physics, Book 48
ISBN13: 9783110597295
Publisher: De Gruyter
Published: Aug 21 2018
Pages: 348
Weight: 1.67
Height: 0.81 Width: 6.69 Depth: 9.61
Language: English
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.
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