# Search Results for "the-dynamical-system-generated-by-the-3n-1-function-lecture-notes-in-mathematics"

## The Dynamical System Generated by the 3n+1 Function

**Author**: Günther J. Wirsching**Publisher:**Springer**ISBN:**3540696776**Category:**Mathematics**Page:**164**View:**4868

The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.

## Unsolved Problems in Number Theory

**Author**: Richard Guy**Publisher:**Springer Science & Business Media**ISBN:**0387266771**Category:**Mathematics**Page:**438**View:**1229

Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.

## The Mathematics of Oz

*Mental Gymnastics from Beyond the Edge*

**Author**: Clifford A. Pickover**Publisher:**Cambridge University Press**ISBN:**9780521016780**Category:**Games & Activities**Page:**351**View:**5543

Filled with an abundance of complex mysteries, sequences, series, puzzles, mazes, and problems, a perplexing journey through the realm of math, mind, and meaning with the author, Dorothy, and Dr. Oz introduces readers to numbers and their role in creativity, computers, games, and practical research. (Science & Mathematics)

## Introduction to Functional Differential Equations

**Author**: Jack K. Hale,Sjoerd M. Verduyn Lunel,Lunel S. Verduyn,Sjoerd M.. Verduyn Lunel**Publisher:**Springer Science & Business Media**ISBN:**9780387940762**Category:**Mathematics**Page:**447**View:**6065

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

## The Art of Random Walks

**Author**: Andras Telcs**Publisher:**Springer Science & Business Media**ISBN:**3540330275**Category:**Mathematics**Page:**195**View:**3459

Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality.

## Introduction to Symplectic Dirac Operators

**Author**: Katharina Habermann,Lutz Habermann**Publisher:**Springer**ISBN:**3540334211**Category:**Mathematics**Page:**125**View:**9435

This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.

## Discrete and Continuous Dynamical Systems

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Differentiable dynamical systems**Page:**N.A**View:**8569

## Dynamics of Continuous, Discrete & Impulsive Systems

*Mathematical analysis*

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Control theory**Page:**N.A**View:**2592

## Evolutionary Equations with Applications in Natural Sciences

**Author**: Jacek Banasiak,Mustapha Mokhtar-Kharroubi**Publisher:**Springer**ISBN:**3319113224**Category:**Mathematics**Page:**493**View:**350

With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.

## Reviews in global analysis, 1980-86 as printed in Mathematical reviews

**Author**: American Mathematical Society**Publisher:**N.A**ISBN:**N.A**Category:**Global analysis (Mathematics)**Page:**3920**View:**3517

## Fifteen Papers on Analysis

**Author**: V. I. Arnol'd**Publisher:**American Mathematical Soc.**ISBN:**9780821896334**Category:****Page:**N.A**View:**4438

## From Finite to Infinite Dimensional Dynamical Systems

*[proceedings of the NATO Advanced Study Institute on From Finite to Infinite Dimensional Dynamic Systems, Cambridge, United Kingdom, 21 August-1 September 1995)]*

**Author**: North Atlantic Treaty Organization. Scientific Affairs Division**Publisher:**Springer Science & Business Media**ISBN:**9780792369752**Category:**Mathematics**Page:**215**View:**8171

The central theme of this book is how ideas familiar from finite dimensional dynamical systems may be used in the study of infinite dimensional dynamical systems, such as partial differential equations. After an introduction to the study of partial differential equations from the perspective of dynamical systems, some of the ideas are applied to the equations of fluid dynamics and the application of low-dimensional models of turbulence. A discussion of chaos in lattice dynamical systems (for which the spatial dimension is discrete) is followed by the use of such models in biology. The book provides an introduction to a range of new techniques and applications in dynamics and will interest any graduate student starting work in the area, as well as more experienced scientists and mathematicians keen to extend their knowledge.

## Twisted Teichmüller Curves

**Author**: Christian Weiß**Publisher:**Springer**ISBN:**3319040758**Category:**Mathematics**Page:**166**View:**2703

These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmüller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. These new objects are analyzed in detail and their main properties are described. In particular, the volume of twisted Teichmüller curves is calculated and their components are partially classified. The study of algebraic curves on Hilbert modular surfaces has been widely covered in the literature due to their arithmetic importance. Among these, twisted diagonals (Hirzebruch-Zagier cycles) are some of the most important examples.

## Risks and safety in economic systems

**Author**: N.A**Publisher:**LLC IPC Bon Anza**ISBN:**590314022X**Category:**Economics**Page:**394**View:**995

## Substitution Dynamical Systems - Spectral Analysis

**Author**: Martine Queffélec**Publisher:**Springer**ISBN:**3642112129**Category:**Mathematics**Page:**351**View:**488

This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.

## Geometric Theory of Discrete Nonautonomous Dynamical Systems

**Author**: Christian Pötzsche**Publisher:**Springer Science & Business Media**ISBN:**3642142575**Category:**Mathematics**Page:**399**View:**429

The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).