Dynamical Systems and Geometric Mechanics

An Introduction

Jared Maruskin

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English

De Gruyter
21 August 2018

Differential calculus & equations; Topology; Classical mechanics; Mathematical physics

Series: De Gruyter Studies in Mathematical Physics

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.

By: Jared Maruskin
Imprint: De Gruyter
Country of Publication: Germany
Edition: 2nd ed.
Volume: 48
Dimensions: Height: 240mm, Width: 170mm, Spine: 21mm
Weight: 733g
ISBN: 9783110597295
ISBN 10: 3110597292
Series: De Gruyter Studies in Mathematical Physics
Pages: 348
Publication Date: 21 August 2018
Audience: College/higher education , A / AS level , Undergraduate
Format: Hardback
Publisher's Status: Active

Jared Michael Maruskin, MZ Inc., USA

Reviews for Dynamical Systems and Geometric Mechanics: An Introduction

This book is exceptionally well-written. It also has an extensive and excellent bibliography. William J. Satzer Jr. in: Zentralblatt fur Mathematik 1402.37001