LEADER 03807nam 22005895 450 001 9910897980103321 005 20260121094114.0 010 $a3-031-67495-2 024 7 $a10.1007/978-3-031-67495-2 035 $a(MiAaPQ)EBC31731099 035 $a(Au-PeEL)EBL31731099 035 $a(CKB)36364865500041 035 $a(DE-He213)978-3-031-67495-2 035 $a(EXLCZ)9936364865500041 100 $a20241017d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDynamics of Circle Mappings /$fby Edson de Faria, Pablo Guarino 205 $a2nd ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (462 pages) 225 1 $aIMPA Monographs 311 08$a3-031-67494-4 327 $aPreface -- Part I - Basic Theory: 1 Rotations -- 2 Homeomorphisms of the Circle -- Part II - Diffeomorphisms: 3 Diffeomorphisms: Denjoy Theory -- 4 Smooth Conjugacies to Rotations -- Part III - Multicritical Circle Maps -- 5 Cross-ratios and Distortion Tools -- 6 Topological Classification and the Real Bounds -- 7 Quasisymmetric Rigidity -- 8 Ergodic Aspects -- 9 Orbit Flexibility -- Part IV - Renormalization Theory: 10 Smooth Rigidity and Renormalization. -- 11 Quasiconformal Deformations -- 12 Lipschitz Estimates for Renormalization -- 13 Exponential Convergence: the Smooth Case -- 14 Renormalization: Holomorphic Methods -- Epilogue -- Appendices -- Bibliography. 330 $aThis book explores recent developments in the dynamics of invertible circle maps, a rich and captivating topic in one-dimensional dynamics. It focuses on two main classes of invertible dynamical systems on the circle: global diffeomorphisms and smooth homeomorphisms with critical points. The latter is the book's core, reflecting the authors' recent research interests. Organized into four parts and 14 chapters, the content covers rigid rotations, circle homeomorphisms, and the concept of rotation number in the first part. The second part delves into circle diffeomorphisms, presenting classical results. The third part introduces multicritical circle maps?smooth homeomorphisms of the circle with a finite number of critical points. The fourth and final part centers on renormalization theory, analyzing the fine geometric structure of orbits of multicritical circle maps. Complete proofs for several fundamental results in circle dynamics are provided throughout. The book concludes with a list of open questions. Primarily intended for graduate students and young researchers in dynamical systems, this book is also suitable for mathematicians from other fields with an interest in the subject. Prerequisites include familiarity with the content of a standard graduate course in real analysis, along with some understanding of ergodic theory and dynamical systems. Basic knowledge of complex analysis is needed for specific chapters. 410 0$aIMPA Monographs 606 $aDynamics 606 $aDynamical Systems 606 $aDinàmica$2thub 606 $aEspais de Teichmüller$2thub 606 $aFuncions holomorfes$2thub 606 $aFuncions de variables complexes$2thub 608 $aLlibres electrònics$2thub 615 0$aDynamics. 615 14$aDynamical Systems. 615 7$aDinàmica 615 7$aEspais de Teichmüller 615 7$aFuncions holomorfes 615 7$aFuncions de variables complexes 676 $a515.39 700 $aFaria$b Edson de$0472693 701 $aGuarino$b Pablo$01766784 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910897980103321 996 $aDynamics of Circle Mappings$94211507 997 $aUNINA