04525nam 22008295 450 991025407570332120200630093521.03-319-29662-010.1007/978-3-319-29662-3(CKB)3710000000649164(EBL)4509026(SSID)ssj0001666035(PQKBManifestationID)16455490(PQKBTitleCode)TC0001666035(PQKBWorkID)15000167(PQKB)10366102(DE-He213)978-3-319-29662-3(MiAaPQ)EBC4509026(PPN)193444364(EXLCZ)99371000000064916420160418d2016 u| 0engur|n|---|||||txtccrThe Parameterization Method for Invariant Manifolds From Rigorous Results to Effective Computations /by Àlex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (280 p.)Applied Mathematical Sciences,0066-5452 ;195Description based upon print version of record.3-319-29660-4 Includes bibliographical references and index.An Overview of the Parameterization Method for Invariant Manifolds -- Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points -- The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics -- The Parameterization Method in KAM Theory -- A Newton-like Method for Computing Normally Hyperbolic Invariant Tori.This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples,  many of them well known in the literature of numerical computation in dynamical systems.  A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and  applications of computational dynamical systems.Applied Mathematical Sciences,0066-5452 ;195DynamicsErgodic theoryStatistical physicsDynamicsNumerical analysisDifferential equations, PartialDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XComplex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Dynamics.Ergodic theory.Statistical physics.Dynamics.Numerical analysis.Differential equations, Partial.Dynamical Systems and Ergodic Theory.Complex Systems.Numerical Analysis.Partial Differential Equations.Statistical Physics and Dynamical Systems.515.42Haro Àlexauthttp://id.loc.gov/vocabulary/relators/aut947680Canadell Martaauthttp://id.loc.gov/vocabulary/relators/autFigueras Jordi-Lluisauthttp://id.loc.gov/vocabulary/relators/autLuque Alejandroauthttp://id.loc.gov/vocabulary/relators/autMondelo Josep Mariaauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254075703321The Parameterization Method for Invariant Manifolds2141276UNINA