Causality: The p-adic Theory / by Vladimir Anashin.

Format:

Book

Author/Creator:

Anashin, Vladimir, Author.

Series:

STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, 2520-1948

Language:

English

Subjects (All):

Number theory.

Mathematical analysis.

Dynamics.

Sequences (Mathematics).

Number Theory.

Analysis.

Dynamical Systems.

Sequences, Series, Summability.

Local Subjects:

Number Theory.

Analysis.

Dynamical Systems.

Sequences, Series, Summability.

Physical Description:

1 online resource (XXVI, 413 p. 54 illus., 42 illus. in color.)

Edition:

1st ed. 2025.

Place of Publication:

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

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-85818-2

OCLC:

1524424609