Dynamics of Circle Mappings

Edson de Faria graduated with a B.Sc. in Physics at the University of São Paulo (USP) and received his Ph.D. in Mathematics from the City University of New York (CUNY), studying with Dennis Sullivan. He held postdoctoral positions at the Institute for Advanced Study in Princeton, ETH-Zürich, IHES and SUNY at Stony-Brook, and later visiting professorships at CUNY and Imperial College London. He is currently a Full Professor at USP.  His research deals primarily with low-dimensional dynamical systems.Pablo Guarino graduated in Mathematics in Uruguay, where he began to study Dynamical Systems. He then moved to Rio de Janeiro, to work on his Ph.D. at the Institute of Pure and Applied Mathematics (IMPA). He learned one-dimensional dynamics from his advisor, Welington de Melo, and his interest in the area persists to this day. He was a postdoctoral fellow at the Institute of Mathematics and Statistics of the University of São Paulo (IME-USP). His Ph.D. thesis was awarded in 2013 with the CAPES Best Thesis Prize and the Carlos Gutierrez Prize, given by ICMC-USP, Brazil. He is currently an Assistant Professor at Fluminense Federal University (UFF), in the state of Rio de Janeiro.

• Preface.- 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.