Dynamical Systems
Examples of Complex Behaviour
Jost, Jürgen.
creator
author.
aut
http://id.loc.gov/vocabulary/relators/aut
SpringerLink (Online service)
text
gw
2005
monographic
eng
access
VIII, 190 p. 65 illus., 15 illus. in color. online resource.
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.
Stability of dynamical systems, bifurcations, and generic properties -- Discrete invariants of dynamical systems -- Entropy and topological aspects of dynamical systems -- Entropy and metric aspects of dynamical systems -- Entropy and measure theoretic aspects of dynamical systems -- Smooth dynamical systems -- Cellular automata and Boolean networks as examples of discrete dynamical systems.
by Jürgen Jost.
Physics
Mathematics
Differentiable dynamical systems
Operations research
Economic theory
Mathematical optimization
Physics, general
Mathematics, general
Dynamical Systems and Ergodic Theory
Operations Research/Decision Theory
Economic Theory/Quantitative Economics/Mathematical Methods
Calculus of Variations and Optimal Control; Optimization
QC1-75
530
Springer eBooks
Universitext
9783540288893
https://doi.org/10.1007/3-540-28889-9
https://doi.org/10.1007/3-540-28889-9
ISI Library, Kolkata
100301
20181203160143.0
978-3-540-28889-3