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010   $a3-031-84828-4
024 7 $a10.1007/978-3-031-84828-5
035   $a(CKB)39664117100041
035   $a(MiAaPQ)EBC32227371
035   $a(Au-PeEL)EBL32227371
035   $a(DE-He213)978-3-031-84828-5
035   $a(OCoLC)1530384539
035   $a(EXLCZ)9939664117100041
100   $a20250716d2025      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aChaotic Maps, Fractals, and Rapid Fluctuations $eWith Applications to Chaotic Vibration of the Wave Equation /$fby Liangliang Li, Yu Huang, Goong Chen
205   $a2nd ed. 2025.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025.
215   $a1 online resource (406 pages)
225 1 $aSynthesis Lectures on Mathematics & Statistics,$x1938-1751
311 08$a3-031-84827-6 
327   $aSimple Interval Maps and Their Iterations -- Total Variations of Iterates of Maps -- Ordering among Periods: The Sharkovski Theorem -- Bifurcation Theorems for Maps -- Homoclinicity. Lyapunoff Exponents -- Symbolic Dynamics, Conjugacy and Shift Invariant Sets -- The Smale Horseshoe -- Fractals -- Rapid Fluctuations of Chaotic Maps on RN -- Infinite-dimensional Systems Induced by Continuous-Time Difference Equations.
330   $aThis book was developed from lecture notes for an introductory graduate course and provides an essential introduction to chaotic maps in finite-dimensional spaces. Furthermore, the authors show how to apply this theory to infinite-dimensional systems corresponding to partial differential equations to study chaotic vibration of the wave equation subject to various types of nonlinear boundary conditions. The book provides background on chaos as a highly interesting nonlinear phenomenon and explains why it is one of the most important scientific findings of the past three decades. In addition, the book covers key topics including one-dimensional dynamical systems, bifurcations, general topological, symbolic dynamical systems, and fractals. The authors also show a class of infinite-dimensional nonlinear dynamical systems, which are reducible to interval maps, plus rapid fluctuations of chaotic maps. This second edition includes updated and expanded chapters as well as additional problems. In addition, this book: ? Provides an overview of chaos in a comprehensive way and contains applications to partial differential equations ? Includes numerous problems allowing readers to practice and apply the presented concepts ? Focuses on presenting the material in a concise, easily readable way that is suitable for a beginning textbook About the Authors Liangliang Li, Ph.D., is an Associate Professor at Sun Yat-Sen University. Yu Huang, Ph.D., is an Associate Professor at Sun Yat-Sen University. Goong Chen, Ph.D., is a Professor of Mathematics at Texas A&M University in Qatar at Doha, Qatar.
410  0$aSynthesis Lectures on Mathematics & Statistics,$x1938-1751
606   $aDynamics
606   $aEngineering mathematics
606   $aMathematical analysis
606   $aTopology
606   $aDynamics
606   $aNonlinear theories
606   $aMathematics
606   $aDynamical Systems
606   $aEngineering Mathematics
606   $aAnalysis
606   $aTopology
606   $aApplied Dynamical Systems
606   $aMathematics
615  0$aDynamics.
615  0$aEngineering mathematics.
615  0$aMathematical analysis.
615  0$aTopology.
615  0$aDynamics.
615  0$aNonlinear theories.
615  0$aMathematics.
615 14$aDynamical Systems.
615 24$aEngineering Mathematics.
615 24$aAnalysis.
615 24$aTopology.
615 24$aApplied Dynamical Systems.
615 24$aMathematics.
676   $a515.39
700   $aLi$b Liangliang$01835004
701   $aHuang$b Yu$01060523
701   $aChen$b Goong$066188
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9911015621803321
996   $aChaotic Maps, Fractals, and Rapid Fluctuations$94410699
997   $aUNINA