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Lyapunov stability of transformation semigroups

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Lyapunov stability of transformation semigroups/ by Victor H. L. Rocha, Josiney A. Souza.
Author:	Rocha, Victor H. L.
other author:	Souza, Josiney A.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xviii, 228 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Lyapunov stability. -
Online resource:	https://doi.org/10.1007/978-3-031-85761-4
ISBN:	9783031857614

Lyapunov stability of transformation semigroups
Rocha, Victor H. L.

Lyapunov stability of transformation semigroups[electronic resource] /by Victor H. L. Rocha, Josiney A. Souza. - Cham :Springer Nature Switzerland :2025. - xviii, 228 p. :ill., digital ;24 cm. - Latin American mathematics series,2524-6763. - Latin American mathematics series..

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.

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.

ISBN: 9783031857614

Standard No.: 10.1007/978-3-031-85761-4doiSubjects--Topical Terms:

745741
Lyapunov stability.

LC Class. No.: QA871

Dewey Class. No.: 515.392

Lyapunov stability of transformation semigroups
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520 $a 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.
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