LEADER 04510nam 22006375 450 001 9910254571903321 005 20200630003231.0 010 $a3-319-51893-3 024 7 $a10.1007/978-3-319-51893-0 035 $a(CKB)3710000001124872 035 $a(DE-He213)978-3-319-51893-0 035 $a(MiAaPQ)EBC4831983 035 $a(PPN)199767459 035 $a(EXLCZ)993710000001124872 100 $a20170327d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPredictability of Chaotic Dynamics $eA Finite-time Lyapunov Exponents Approach /$fby Juan C. Vallejo, Miguel A. F. Sanjuan 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XV, 136 p. 47 illus., 22 illus. in color.) 225 1 $aSpringer Series in Synergetics,$x0172-7389 311 $a3-319-51892-5 320 $aIncludes bibliographical references. 327 $aPreface -- Forecasting and Chaos -- Lyapunov Exponents -- Dynamical Regimes and Timescales -- Predictability -- Numerical Calculation of Lyapunov Exponents. 330 $aThis book is primarily concerned with the computational aspects of predictability of dynamical systems ? in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for instance in celestial mechanics, one is confronted with the observation and modeling of systems without the possibility of altering the key parameters of the objects studied. Therefore, the numerical simulations offer an essential tool for analyzing these systems. With the widespread use of computer simulations to solve complex dynamical systems, the reliability of the numerical calculations is of ever-increasing interest and importance. This reliability is directly related to the regularity and instability properties of the modeled flow. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the finite-time Lyapunov exponents approach. The method is illustrated using a number of well-known continuous dynamical systems, including the Contopoulos, Hénon-Heiles and Rössler systems. To help students and newcomers quickly learn to apply these techniques, the appendix provides descriptions of the algorithms used throughout the text and details how to implement them in order to solve a given continuous dynamical system. 410 0$aSpringer Series in Synergetics,$x0172-7389 606 $aStatistical physics 606 $aPhysics 606 $aSpace sciences 606 $aMathematical physics 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aSpace Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)$3https://scigraph.springernature.com/ontologies/product-market-codes/P22030 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aStatistical physics. 615 0$aPhysics. 615 0$aSpace sciences. 615 0$aMathematical physics. 615 14$aApplications of Nonlinear Dynamics and Chaos Theory. 615 24$aNumerical and Computational Physics, Simulation. 615 24$aSpace Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). 615 24$aMathematical Applications in the Physical Sciences. 676 $a003.857 700 $aVallejo$b Juan C$4aut$4http://id.loc.gov/vocabulary/relators/aut$0823845 702 $aSanjuan$b Miguel A. F$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254571903321 996 $aPredictability of Chaotic Dynamics$91982581 997 $aUNINA