Lyapunov Stability of Transformation Semigroups / by Victor H. L. Rocha, Josiney A. Souza.

Format:

Book

Author/Creator:

Rocha, Victor H. L., Author.

Souza, Josiney A., Author.

Series:

Latin American Mathematics Series, 2524-6763

Language:

English

Subjects (All):

Dynamics.

System theory.

Control theory.

Dynamical Systems.

Systems Theory, Control.

Local Subjects:

Dynamical Systems.

Systems Theory, Control.

Physical Description:

1 online resource (XVIII, 228 p. 14 illus.)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This book presents recent research results on Lyapunov stability and attraction for semigroup actions in a pedagogical format, providing the reader with numerous modern ideas and mathematical formulations for dynamical concepts in the transformation group theory. In recent decades, many fundamental concepts of dynamical systems have been extended to the general framework of transformation semigroups. Limit sets, attractors, isolated invariant sets, prolongational limit sets, and stable sets now have semigroup theoretical analogues. This monograph consolidates recent advancements in this field in a way that makes it accessible to graduate students. An effort was made to relate the presented results to important recurrence notions, for contextual clarity. A rudimentary understanding of group theory and topology, including the concepts of semigroup action, orbit, fiber bundle, compactness, and connectedness, is a prerequisite for reading this text. As a valuable resource for research projects and academic dissertations on topological dynamics, geometry, and mathematical analysis, this work can potentially open new avenues for further research.

Contents:

Preface

Introduction

Semigroup actions

Attraction and Lyapunov stability

Orbital maps

Lyapunov stability on fiber bundles

Fenichel’s uniformity lemma

Stability and controllability

Higher stability and generalized recurrence

Fiber bundles

References

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-85761-5

OCLC:

1524421462