e-book Quasiconformal Surgery in Holomorphic Dynamics (Cambridge Studies in Advanced Mathematics)

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We prove that has at least two disjoint and infinite critical orbits in the Julia set if it has a Herman ring.

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This result is sharp in the following sense: there exists a cubic rational map having exactly two critical grand orbits but also having a Herman ring. In particular, has no Herman rings if it has at most one infinite critical orbit in the Julia set.

Holomorphic Dynamics

These criterions derive some known results about the rational maps without Herman rings. References [Enhancements On Off] What's this? Petersen, Kevin M. Pilgrim, Tan Lei and Michael Yampolsky. Derrida , L. Itzykson , Fractal structure of zeros in hierarchical models , J. Devaney , Daniel M. Look , and David Uminsky , The escape trichotomy for singularly perturbed rational maps , Indiana Univ. Devaney and E. Theory Appl. Lyubich , Dynamics of rational transformations: topological picture , Uspekhi Mat. Nauk 41 , no.


  • AMS :: Conformal Geometry and Dynamics of the American Mathematical Society.
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Surveys trends arising from the applications and interactions between combinatorics, symbolic dynamics and theoretical computer science. A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations. Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.

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This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics. Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics. A broad introduction, perfect for a one-year graduate course.

Includes examples to motivate the theory and some remarkable applications. This rigorous undergraduate introduction to dynamical systems is an accessible guide for mathematics students advancing from calculus. Presents the major mathematical tools necessary for the study of complex dynamics. A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Constructing entire functions by quasiconformal folding | SpringerLink

Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics. An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.

Covers an area at intersection of probability theory and statistical mechanics.