04124nam a22005895i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003100137040002500168050001100193072001500204072002300219072001400242082001200256100007700268245009900345264006100444300006600505336002600571337002600597338003600623347002400659490002900683505039900712520125001111650001302361650001702374650003802391650002502429650002102454650003102475650009302506650009702599650011302696650011202809650013602921650013303057710003403190773002003224776003603244776003603280830002903316856004203345912001403387942000703401950004803408999001903456952005903475978-3-540-28889-3DE-He21320181203160143.0cr nn 008mamaa100301s2005 gw | s |||| 0|eng d a97835402888939978-3-540-28889-37 a10.1007/3-540-28889-92doi aISI Library, Kolkata 4aQC1-75 7aPH2bicssc 7aSCI0550002bisacsh 7aPH2thema04a5302231 aJost, Jürgen.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aDynamical Systemsh[electronic resource] :bExamples of Complex Behaviour /cby Jürgen Jost. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2005. aVIII, 190 p. 65 illus., 15 illus. in color.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUniversitext,x0172-59390 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. 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. 0aPhysics. 0aMathematics. 0aDifferentiable dynamical systems. 0aOperations research. 0aEconomic theory. 0aMathematical optimization.14aPhysics, general.0http://scigraph.springernature.com/things/product-market-codes/P0000224aMathematics, general.0http://scigraph.springernature.com/things/product-market-codes/M0000924aDynamical Systems and Ergodic Theory.0http://scigraph.springernature.com/things/product-market-codes/M1204X24aOperations Research/Decision Theory.0http://scigraph.springernature.com/things/product-market-codes/52100024aEconomic Theory/Quantitative Economics/Mathematical Methods.0http://scigraph.springernature.com/things/product-market-codes/W2900024aCalculus of Variations and Optimal Control; Optimization.0http://scigraph.springernature.com/things/product-market-codes/M260162 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978354080348508iPrinted edition:z9783540229087 0aUniversitext,x0172-593940uhttps://doi.org/10.1007/3-540-28889-9 aZDB-2-SMA cEB aMathematics and Statistics (Springer-11649) c424954d424954 9275543aMAINbMAINd2017-04-01pEB1095r2018-12-03yEB