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001439256 001__ 1439256
001439256 003__ OCoLC
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001439256 019__ $$a1266905167
001439256 020__ $$a9789811635441$$q(electronic bk.)
001439256 020__ $$a9811635447$$q(electronic bk.)
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001439256 0247_ $$a10.1007/978-981-16-3544-1$$2doi
001439256 035__ $$aSP(OCoLC)1265524726
001439256 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dEBLCP$$dNOC$$dGW5XE$$dOCLCO$$dOCLCF$$dUKAHL$$dOCLCO$$dOCLCQ$$dCOM$$dOCLCQ
001439256 049__ $$aISEA
001439256 050_4 $$aQC174.85.S34
001439256 08204 $$a530.15/95$$223
001439256 1001_ $$aLeonel, Edson Denis,$$eauthor
001439256 24510 $$aScaling laws in dynamical systems /$$cEdson Denis Leonel
001439256 264_1 $$aSingapore :$$bSpringer,$$c2021.
001439256 300__ $$a1 online resource
001439256 336__ $$atext$$btxt$$2rdacontent
001439256 337__ $$acomputer$$bc$$2rdamedia
001439256 338__ $$aonline resource$$bcr$$2rdacarrier
001439256 4901_ $$aNonlinear Physical Science
001439256 504__ $$aIncludes bibliographical references.
001439256 5050_ $$aIntro -- Preface -- Acknowledgements -- Contents -- List of Figures -- List of Tables -- 1 Introduction -- 1.1 Initial Concepts -- 1.2 Summary -- 2 One-Dimensional Mappings -- 2.1 Introduction -- 2.2 The Concept of Stability -- 2.2.1 Asymptotically Stable Fixed Point -- 2.2.2 Neutral Stability -- 2.2.3 Unstable Fixed Point -- 2.3 Fixed Points to the Logistic Map -- 2.4 Bifurcations -- 2.4.1 Transcritical Bifurcation -- 2.4.2 Period Doubling Bifurcation -- 2.4.3 Tangent Bifurcation -- 2.5 Summary -- 2.6 Exercises -- 3 Some Dynamical Properties for the Logistic Map
001439256 5058_ $$a5.1 Linear Mappings -- 5.2 Nonlinear Mappings -- 5.3 Applications of Two Dimensional Mappings -- 5.3.1 Hénon Map -- 5.3.2 Lyapunov Exponents -- 5.3.3 Ikeda Map -- 5.4 Summary -- 5.5 Exercises -- 6 A Fermi Accelerator Model -- 6.1 Fermi-Ulam Model -- 6.1.1 Jacobian Matrix for the Indirect Collisions -- 6.1.2 Jacobian Matrix for the Direct Collisions -- 6.1.3 Fixed Points -- 6.1.4 Phase Space -- 6.1.5 Phase Space Measure Preservation -- 6.2 A Simplified Version of the Fermi-Ulam Model -- 6.3 Scaling Properties for the Chaotic Sea -- 6.4 Localization of the First Invariant Spanning Curve
001439256 506__ $$aAccess limited to authorized users.
001439256 520__ $$aThis book discusses many of the common scaling properties observed in some nonlinear dynamical systems mostly described by mappings. The unpredictability of the time evolution of two nearby initial conditions in the phase space together with the exponential divergence from each other as time goes by lead to the concept of chaos. Some of the observables in nonlinear systems exhibit characteristics of scaling invariance being then described via scaling laws. From the variation of control parameters, physical observables in the phase space may be characterized by using power laws that many times yield into universal behavior. The application of such a formalism has been well accepted in the scientific community of nonlinear dynamics. Therefore I had in mind when writing this book was to bring together few of the research results in nonlinear systems using scaling formalism that could treated either in under-graduation as well as in the post graduation in the several exact programs but no earlier requirements were needed from the students unless the basic physics and mathematics. At the same time, the book must be original enough to contribute to the existing literature but with no excessive superposition of the topics already dealt with in other text books. The majority of the Chapters present a list of exercises. Some of them are analytic and others are numeric with few presenting some degree of computational complexity.
001439256 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed September 9, 2021).
001439256 650_0 $$aScaling laws (Statistical physics)
001439256 650_0 $$aNonlinear mechanics.
001439256 650_6 $$aLois d'échelle (Physique statistique)
001439256 650_6 $$aMécanique non linéaire.
001439256 655_0 $$aElectronic books.
001439256 77608 $$iPrint version:$$aLeonel, Edson Denis.$$tScaling laws in dynamical systems.$$dSingapore : Springer, 2021$$z9811635439$$z9789811635434$$w(OCoLC)1252414377
001439256 830_0 $$aNonlinear physical science.
001439256 852__ $$bebk
001439256 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-16-3544-1$$zOnline Access$$91397441.1
001439256 909CO $$ooai:library.usi.edu:1439256$$pGLOBAL_SET
001439256 980__ $$aBIB
001439256 980__ $$aEBOOK
001439256 982__ $$aEbook
001439256 983__ $$aOnline
001439256 994__ $$a92$$bISE