Dynamical Systems and Geometric Mechanics

An Introduction
2. Auflage 2025
ISBN: 978-3-11-059729-5
Verlag: De Gruyter

Buch, Englisch, 336 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 771 g

Reihe: ISSN

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.

Zielgruppe

Researchers in Mathematical and Theoretical Physics, and Mathemat

Autoren/Hrsg.

Maruskin, Jared

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Über Autor(innen)

Jared Michael Maruskin, MZ Inc., USA