Andere Kunden interessierten sich auch für
![Introduction to Hyperbolic Geometry]( "Introduction to Hyperbolic Geometry")
Introduction to Hyperbolic Geometry53,99 €![Fuzzy Logic and Its Applications to Engineering, Information Sciences, and Intelligent Systems]( "Fuzzy Logic and Its Applications to Engineering, Information Sciences, and Intelligent Systems")
Fuzzy Logic and Its Applications to Engineering, Information Sciences, and Intelligent Systems107,99 €![Proof Theory]( "Proof Theory")
Proof Theory52,99 €![Logical Number Theory I]( "Logical Number Theory I")
Logical Number Theory I62,99 €![Fuzzy Geometric Programming]( "Fuzzy Geometric Programming")
Fuzzy Geometric Programming120,99 €![Machines, Computations, and Universality]( "Machines, Computations, and Universality")
Machines, Computations, and Universality125,99 €![Optimization Models Using Fuzzy Sets and Possibility Theory]( "Optimization Models Using Fuzzy Sets and Possibility Theory")
Optimization Models Using Fuzzy Sets and Possibility Theory104,99 €
This book presents a survey of the field of dynamical systems and its significance for research in complex systems and other fields, based on a careful analysis of specific important examples. It also explains the fundamental underlying mathematical concepts, with a particular focus on invariants of dynamical systems, including a systematic treatment of Morse-Conley theory. Entropy and related concepts in the topological, metric, measure theoretic and smooth settings and some connections with information theory are discussed, and cellular automata and random Boolean networks are presented as specific examples.
Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some ?nal or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyoftheconceptstobeintroducedareusefulineither case.
Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some ?nal or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyoftheconceptstobeintroducedareusefulineither case.
"This book provides a survey of various topics of dynamical systems. Applications of both the concepts and the results are presented.
The author takes the opportunity to explain the underlying fundamental mathematical concepts involved in the results, for example the Conley-Floer theory, which is a topic that is not commonly studied in introductory texts on dynamical systems. The book studies entropy and related concepts within topological, metric, measure theoretic and smooth settings, giving connections with information theory, cellular automata and Boolean networks.
The book is written in a careful style. Most of the results are given without proof, though the necessary references for them are included. Many of the results are illustrated through carefully chosen examples." (Sergio Plaza, Mathematical Reviews)
The author takes the opportunity to explain the underlying fundamental mathematical concepts involved in the results, for example the Conley-Floer theory, which is a topic that is not commonly studied in introductory texts on dynamical systems. The book studies entropy and related concepts within topological, metric, measure theoretic and smooth settings, giving connections with information theory, cellular automata and Boolean networks.
The book is written in a careful style. Most of the results are given without proof, though the necessary references for them are included. Many of the results are illustrated through carefully chosen examples." (Sergio Plaza, Mathematical Reviews)