03383nam 22006135 450 991099649070332120260204152639.03-031-85761-510.1007/978-3-031-85761-4(CKB)38337906600041(DE-He213)978-3-031-85761-4(MiAaPQ)EBC32006592(Au-PeEL)EBL32006592(EXLCZ)993833790660004120250410d2025 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierLyapunov Stability of Transformation Semigroups /by Victor H. L. Rocha, Josiney A. Souza1st ed. 2025.Cham :Springer Nature Switzerland :Imprint: Springer,2025.1 online resource (XVIII, 228 p. 14 illus.)Latin American Mathematics Series,2524-67633-031-85760-7 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.Latin American Mathematics Series,2524-6763DynamicsSystem theoryControl theoryDynamical SystemsSystems Theory, ControlGrups de transformacionsthubSemigrupsthubLlibres electrònicsthubDynamics.System theory.Control theory.Dynamical Systems.Systems Theory, Control.Grups de transformacionsSemigrups515.39Rocha Victor H. Lauthttp://id.loc.gov/vocabulary/relators/aut1817587Souza Josiney Aauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910996490703321Lyapunov Stability of Transformation Semigroups4375475UNINA