03014nmm a2200397 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001800139245009500157250001700252260006300269300006400332505039800396653002400794653002500818653006100843653002100904653004100925653001200966653003700978653002001015653004001035653006401075653001601139653003001155710003401185041001901219989003601238490001701274856006801291082000801359520124901367EB000374015EBX0100000000000000022706700000000000000.0cr|||||||||||||||||||||130626 ||| eng a97835402888931 aJost, Jürgen00aDynamical SystemshElektronische RessourcebExamples of Complex Behaviourcby Jürgen Jost a1st ed. 2005 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2005, 2005 aVIII, 190 p. 65 illus., 15 illus. in colorbonline resource0 aStability 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 aOperations research aMathematics, general aCalculus of Variations and Optimal Control; Optimization aPhysics, general aDynamical Systems and Ergodic Theory aPhysics aDifferentiable dynamical systems aEconomic theory aOperations Research/Decision Theory aEconomic Theory/Quantitative Economics/Mathematical Methods aMathematics aMathematical optimization2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aUniversitext uhttps://doi.org/10.1007/3-540-28889-9?nosfx=yxVerlag3Volltext0 a530 aOur 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