Causality: The p-adic Theory

• Verfasst von: Anašin, Vladimir S. [VerfasserIn]
• Titel: Causality: The p-adic Theory
• Verf.angabe: by Vladimir Anashin
• Ausgabe: 1st ed. 2025.
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Jahr: 2025
• Umfang: 1 Online-Ressource(XXVI, 413 p. 54 illus., 42 illus. in color.)
• Gesamttitel/Reihe: STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
• ISBN: 978-3-031-85818-5
• DOI: doi:10.1007/978-3-031-85818-5
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Anašin, Vladimir S.: Causality: the p-adic theory. - Cham : Springer Nature Switzerland, 2025. - xxvi, 413 Seiten
• K10plus-PPN: 1924005115
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Foreword -- Preface -- Background -- Part I. Basics of p-Adic Analysis -- Rings and Fields of p-Adic Numbers -- p-Adic Calculus -- p-Adic Series -- 1-Lipschitz functions -- Special Classes of 1-Lipschitz Functions -- Part II. The p-Adic Ergodic Theory -- Ergodic Theory: Preliminaries for the p-Adic Case -- The Main Ergodic Theorem for p-Adic 1-Lipschitz Maps -- 1-Lipschitz Ergodicity on Zp -- Measure-Preservation and Ergodicity of Uniformly Differentiable Functions -- 1-Lipschitz Ergodicity on Subspaces -- Plots of 1-Lipschitz Functions in Euclidean Space -- Part III. Applications -- Applications to Automata Theory -- Applications to Computer Science -- Application to Combinatorics -- Applications to Foundations of Quantum Theory -- References -- Index.

Abstract

This book delves into the mathematical theory of causal functions over discrete time, offering a fresh perspective on causality beyond its philosophical roots. By exploring the intricate world of p-adic 1-Lipschitz functions, this volume bridges the gap between abstract mathematical concepts and their practical applications in fields such as automata theory, combinatorics, and applied computer science. Readers will uncover a wealth of insights as the book investigates key topics including the nature of causal functions, the role of discrete time in causality, and the application of non-Archimedean metrics. With contributions from eminent scholars, this work invites readers to ponder critical questions: How do we define causality in mathematical terms? What are the implications of using p-adic analysis in understanding complex systems especially quantum ones? The author's unique approach makes this book an essential read for anyone interested in the intersection of mathematics and real-world applications. Ideal for researchers and practitioners with a background in mathematics, computer science, or physics, this book is a valuable resource for those seeking to deepen their understanding of causal functions. Whether you're a scholar exploring theoretical perspectives or a professional looking to apply these concepts practically, this volume offers a comprehensive guide to navigating the complexities of causality. Part of an ongoing series on advanced mathematical theories, it is an indispensable addition to any academic library.