TY - BOOK
AU - Jost,Jürgen
ED - SpringerLink (Online service)
TI - Dynamical Systems: Examples of Complex Behaviour
T2 - Universitext,
SN - 9783540288893
AV - QC1-75
U1 - 530 23
PY - 2005///
CY - Berlin, Heidelberg
PB - Springer Berlin Heidelberg
KW - Physics
KW - Mathematics
KW - Differentiable dynamical systems
KW - Operations research
KW - Economic theory
KW - Mathematical optimization
KW - Physics, general
KW - Mathematics, general
KW - Dynamical Systems and Ergodic Theory
KW - Operations Research/Decision Theory
KW - Economic Theory/Quantitative Economics/Mathematical Methods
KW - Calculus of Variations and Optimal Control; Optimization
N1 - 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
N2 - 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
UR - https://doi.org/10.1007/3-540-28889-9
ER -