Causality: The p-adic Theory

Vladimir S. Anashin is a Professor of Mathematics at Lomonosov Moscow State University and a Leading Research Fellow at Federal Research Center ‘Computer Science and Control’ of the Russian Academy of Sciences, Russia. His research interests include non-Archimedean analysis, automata theory, ring theory, group theory as well as applications to computer science and foundations of physics. As a leading expert in the p-adic theory of automata and its applications to computer science and interpretation of quantum mechanics, Prof. Anashin was awarded visiting professorship of Université de Picardie Jules Verne, France (2007) and visiting professorship for Senior International Scientists, Chinese Academy of Sciences (2010-2014), also he was recognized as a Distinguished Lecturer by National Centre of Mathematics and Interdiciplinary Sciences, China (2011).

• 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.