03639nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137040000900172082001500181082001500196100002900211245013500240264004600375300003600421336002600457337002600483338003900509347002400548490005200572505065700624520125001281650001702531650003502548650003802583650003702621650002602658650001702684650004202701650003602743650004402779650001402823700003402837700002902871710003402900773002002934776003602954830005202990856010303042978-0-387-48918-6DE-He21320260521091922.0cr nn 008mamaa100301s2007    xxu|    s    |||| 0|eng d  a9780387489186  a997803874891867 a10.1007/978-0-387-48918-62doi  cCICY04a515.3922304a515.482231 aSanders, Jan A.eauthor.10aAveraging Methods in Nonlinear Dynamical Systemsh[recurso electrónico] /cby Jan A. Sanders, Ferdinand Verhulst, James Murdock. 1aNew York, NY :bSpringer New York,c2007.  aXXIII, 431 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  arecurso en líneabcr2rdacarrier  atext filebPDF2rda1 aApplied Mathematical Sciences,x0066-5452 ;v590 aBasic Material and Asymptotics -- Averaging: the Periodic Case -- Methodology of Averaging -- Averaging: the General Case -- Attraction -- Periodic Averaging and Hyperbolicity -- Averaging over Angles -- Passage Through Resonance -- From Averaging to Normal Forms -- Hamiltonian Normal Form Theory -- Classical (First-Level) Normal Form Theory -- Nilpotent (Classical) Normal Form -- Higher-Level Normal Form Theory -- The History of the Theory of Averaging -- A 4-Dimensional Example of Hopf Bifurcation -- Invariant Manifolds by Averaging -- Some Elementary Exercises in Celestial Mechanics -- On Averaging Methods for Partial Differential Equations.  aPerturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews 0aMATHEMATICS. 0aGLOBAL ANALYSIS (MATHEMATICS). 0aDIFFERENTIABLE DYNAMICAL SYSTEMS. 0aDIFFERENTIAL EQUATIONS, PARTIAL. 0aMATHEMATICAL PHYSICS.14aMATHEMATICS.24aDYNAMICAL SYSTEMS AND ERGODIC THEORY.24aPARTIAL DIFFERENTIAL EQUATIONS.24aMATHEMATICAL AND COMPUTATIONAL PHYSICS.24aANALYSIS.1 aVerhulst, Ferdinand.eauthor.1 aMurdock, James.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387489162 0aApplied Mathematical Sciences,x0066-5452 ;v5940uhttp://dx.doi.org/10.1007/978-0-387-48918-6zVer el texto completo en las instalaciones del CICY