Discontinuous Mapping Dynamics

Erscheinungsjahr 2026
ISBN: 978-981-9250-61-5
Verlag: Springer

Buch, Englisch, 235 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Nonlinear Physical Science

This book systematically presents a theory for the mapping switchability of discontinuous, discrete dynamical systems. In discontinuous discrete systems, there are a set of distinct mappings in ditinct domains. Thus, the problems are how distinct mapping actions can crossover the boundary and get into other domains with mapping switch, and what conditions for the mapping switchability at the boundary can exist in such discontinuous dynamical systems. In this book, the mapping swithcbaility theory is developed, the fully separable and swappable source mapping actions are described, and the switchable and returnable mapping actions are defined as well. The mapping barriers at the boundary are introduced for the source mapping actions and switchable and returnable mapping actions. Finally, the mapping switchability theory to the edge is developed. Using such theory, the Cantor sets and Smale horseshoe sets in topology dynamics can be easily explained.

• Introduced mapping switchability

• Developed mapping switchability and singularity theory

• Presented separable and swappable source mapping actions,

• Presented switchable and returnable mapping actions

• Developed the theory of mapping barriers

• Discussed mapping switchability and attractivity to the edges

• Easy to read

Zielgruppe

Research

Autoren/Hrsg.

Luo, Albert

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Introduction.- Introduction to Discontinuous Discrete Systems.- Mapping Switchability Theory.- Mapping Barriers and Action Switchability.- Mapping Action Switchability at Constraint Edges.

Über Autor(innen)

Professor Albert C. J. Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville (SIUE), USA, and an internationally renowned expert in the field of nonlinear dynamical systems theory and applications. Over the past 30 years, Professor Luo has made seminal contributions to theoretical physics, nonlinear dynamics, and applied mathematics. The novel "toolbox" and "way of thinking" he developed have significantly advanced the understanding of the deep-seated principles governing nonlinear, discontinuous, and complex systems. These contributions include: the theory of planar polynomial dynamical systems and solutions to Hilbert’s 16th problem; stability and bifurcation theory for nonlinear continuous dynamical systems; stability and bifurcation theory for nonlinear discrete dynamical systems; bifurcation dynamics; discontinuous dynamical system theory; generalized synchronization theory for dynamical systems; analytical and semi-analytical methods for periodic and chaotic motions in nonlinear dynamical systems; stochastic layer and resonance layer theory in nonlinear Hamiltonian systems; and dynamics of nonlinear deformable bodies. Professor Luo has published more than 400 peer-reviewed papers in prestigious journals and conference proceedings. He is the author of over 60 monographs and editor of more than 20 volumes. He serves as the editor-in-chief for the series Nonlinear Physical Science (co-published by Higher Education Press and Springer), the series Nonlinear Systems and Complexity (Springer), and the series Chaos, Nonlinearity, and Complexity (World Scientific). He is currently an associate editor for the International Journal of Bifurcation and Chaos and an editorial board member for the AIP journal Chaos.