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#### Geometric Methods for Discrete Dynamical Systems

Oxford University Press 1998; US$ 169.99This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of... more...

#### Fractal Geometry, Complex Dimensions and Zeta Functions

Springer 2007; US$ 89.95Offers a study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. This book interlinks number theory, spectral geometry, and fractal geometry. It gives the Riemann hypothesis a natural geometric reformulation in the context of vibrating fractal strings. It includes theorems, examples and illustrations. more...

#### Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

Springer 2007; US$ 119.00Explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. This book provides an overview of the research in the area. Using geometrical thinking to solve fundamental problems in these areas could be highly productive. more...

#### Piecewise-smooth Dynamical Systems

Springer 2008; US$ 129.00Introduces a framework for understanding the dynamics of piecewise-smooth and hybrid systems. This work presents an introduction, which asserts the ubiquity of such models with examples drawn from mechanics, electronics, control theory and physiology. It classifies complex behavior via bifurcation theory in a systematic yet applicable way. more...

#### Discrete Dynamical Systems

Springer 2007; US$ 59.99Provides an introduction to the analysis of discrete dynamical systems. This book analyzes the factors that govern the quantitative and qualitative behavior of discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for systems that do not permit explicit solutions. more...

#### Topological Theory of Dynamical Systems

Elsevier Science 1994; US$ 72.95This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to... more...

#### Singularities & Dynamical Systems

Elsevier Science 1985; US$ 72.95This volume is an account of the lectures delivered at the international Conference ``Singularities and Dynamical Systems-83''. The main purpose of the Conference was to create conditions of scientific contact between mathematicians and physicists who have singularities and dynamical systems as common interests. more...

#### Dimension and Recurrence in Hyperbolic Dynamics

Springer 2008; US$ 99.00The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative... more...

#### Fractals and Universal Spaces in Dimension Theory

Springer 2009; US$ 119.00Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). This book unifies the modern theory from 1960-2007. more...

#### Iterated Maps on the Interval as Dynamical Systems

Springer 2009; US$ 69.95Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding... more...