Dynamical Systems and Geometric Mechanics: An Introduction

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, Poincar� maps, Floquet theory, the Poincar�-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. Additional ISBNs 3110597292, 3110597802, 9783110597295, 9783110597806Dynamical Systems and Geometric Mechanics: An Introduction 1st Edition is written by Jared Maruskin and published by De Gruyter. ISBNs for Dynamical Systems and Geometric Mechanics are 9783110598032, 3110598035 and the print ISBNs are 9783110597295, 3110597292. Additional ISBNs include 3110597292, 3110597802, 9783110597295, 9783110597806.