03543nam 22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001000172072001700182072002300199082001500222082001500237100002600252245008800278264004600366300003400412336002600446337002600472338003600498347002400534490005300558505025200611520164700863650001702510650001402527650002002541650002502561650002902586650001702615650004202632650003302674700002902707710003402736773002002770776003602790830005302826856004802879912001402927999001902941952007702960978-1-4419-6870-8DE-He21320180115171501.0cr nn 008mamaa101029s2011 xxu| s |||| 0|eng d a97814419687089978-1-4419-6870-87 a10.1007/978-1-4419-6870-82doi 4aQA313 7aPBWR2bicssc 7aMAT0340002bisacsh04a515.3922304a515.482231 aBroer, Henk.eauthor.10aDynamical Systems and Chaosh[electronic resource] /cby Henk Broer, Floris Takens. 1aNew York, NY :bSpringer New York,c2011. aXVI, 313 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aApplied Mathematical Sciences,x0066-5452 ;v1720 aExamples and definitions of dynamical phenomena -- Qualitative properties and predictability of evolutions -- Persistence of dynamical properties -- Global structure of dynamical systems -- On KAM Theory -- Reconstruction and time series analysis. aOver the last four decades there has been extensive development in the theory of dynamical systems. This book starts from the phenomenological point of view reviewing examples. Hence the authors discuss oscillators, like the pendulum in many variation including damping and periodic forcing , the Van der Pol System, the Henon and Logistic families, the Newton algorithm seen as a dynamical system and the Lorenz and Rossler system are also discussed. The phenomena concern equilibrium, periodic, multi- or quasi-periodic and chaotic dynamic dynamics as these occur in all kinds of modeling and are met both in computer simulations and in experiments. The application areas vary from celestial mechanics and economical evolutions to population dynamics and climate variability. The book is aimed at a broad audience of students and researchers. The first four chapters have been used for an undergraduate course in Dynamical Systems and material from the last two chapters and from the appendices has been used for master and PhD courses by the authors. All chapters conclude with an exercise section. One of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory. Henk Broer and Floris Takens, professors at the Institute for Mathematics and Computer Science of the University of Groningen, are leaders in the field of dynamical systems. They have published a wealth of scientific papers and books in this area and both authors are members of the Royal Netherlands Academy of Arts and Sciences (KNAW). 0aMathematics. 0aDynamics. 0aErgodic theory. 0aApplied mathematics. 0aEngineering mathematics.14aMathematics.24aDynamical Systems and Ergodic Theory.24aApplications of Mathematics.1 aTakens, Floris.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781441968692 0aApplied Mathematical Sciences,x0066-5452 ;v17240uhttp://dx.doi.org/10.1007/978-1-4419-6870-8 aZDB-2-SMA c370315d370315 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK