LEADER 04582nam 22006255 450 001 9910349502903321 005 20200630010348.0 010 $a3-030-28630-4 024 7 $a10.1007/978-3-030-28630-9 035 $a(CKB)4100000009678376 035 $a(MiAaPQ)EBC5967259 035 $a(DE-He213)978-3-030-28630-9 035 $a(PPN)248602276 035 $a(EXLCZ)994100000009678376 100 $a20191025d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 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 $a2nd ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (207 pages) $cillustrations 225 1 $aSpringer Series in Synergetics,$x0172-7389 311 $a3-030-28629-0 327 $aPreface -- Forecasting and chaos -- Lyapunov exponents -- Dynamical regimes and timescales -- Predictability -- Chaos, predictability and astronomy -- A detailed example: galactic dynamics -- Appendix. . 330 $aThis book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observations, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, in astronomy it is uncommon to have the possibility of altering the key parameters of the studied objects. Therefore, the numerical simulations offer an essential tool for analysing these systems, and their reliability is of ever-increasing interest and importance. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the strong sensitivity to initial conditions and the use of Lyapunov exponents to characterize this sensitivity. This method is illustrated using several well-known continuous dynamical systems, such as the Contopoulos, Hénon-Heiles and Rössler systems. This second edition revises and significantly enlarges the material of the first edition by providing new entry points for discussing new predictability issues on a variety of areas such as machine decision-making, partial differential equations or the analysis of attractors and basins. Finally, the parts of the book devoted to the application of these ideas to astronomy have been greatly enlarged, by first presenting some basics aspects of predictability in astronomy and then by expanding these ideas to a detailed analysis of a galactic potential. 410 0$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 $a9910349502903321 996 $aPredictability of Chaotic Dynamics$91982581 997 $aUNINA