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Dynamics on the Riemann Sphere presents a collection of original research articles by leading experts in the area of holomorphic dynamics. These papers.
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- Dynamics on the Riemann Sphere: A Bodil Branner Festschrift | Mathematical Association of America
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- Publications and Preprints
Bochi and D. The Ten Martini Problem. Avila, Svetlana Jitomirskaya. Combinatorial rigidity for unicritical polynomials. Avila, Jeremy Kahn, M. Lyubich and Weixiao Shen. Bochi, Amie Wilkinson.
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Annales Scientifiques de l'Ecole Normale Superieure 42 , Uniform exponential growth for some SL 2,R matrix products. Avila, Thomas Roblin. Journal of Modern Dynamics 3 , Density of positive Lyapunov exponents for quasiperiodic SL 2,R cocycles in arbitrary dimension. Almost localization and almost reducibility. Journal of the European Mathematical Society 12 , Extremal Lyapunov exponents: an invariance principle and applications.
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with a. Avila, Barry Simon, Yoram Last. Uniformly hyperbolic finite-valued SL 2,R -cocycles. Bochi, J. Commentarii Mathematici Helvetici 85 , On the regularization of conservative maps. Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Lyubich, W. Journal of the European Mathematical Society 13 , Cohomological equations and invariant distributions for minimal circle diffeomorphisms.
Avila, Alejandro Kocsard. Density of positive Lyapunov exponents for SL 2,R cocycles. Journal of the American Mathematical Society 24 , Avila, Bassam Fayad, R. Geometric and Functional Analysis 21 , The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Mixing for time-changes of Heisenberg nilflows. Avila, G. Forni, Corinna Ulcigrai.
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Journal of Differential Geometry 89 , Bochi, D. Journal of the European Mathematical Society 14 , Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Transactions of the American Mathematical Society , Commentarii Mathematici Helvetici 87 , SL 2,R -invariant probability measures on the moduli spaces of translation surfaces are regular.
Avila, Carlos Matheus, J. Geometric and Functional Analysis 23 , Holonomy invariance: rough regularity and applications to Lyapunov exponents.
Avila, Jimmy Santamaria, M. On rigidity of critical circle maps. Bulletin of the Brazilian Mathematical Society 44 , Damanik, Zhenghe Zhang. Complex one-frequency cocycles. Jitomirskaya, Christian Sadel. Journal of the European Mathematical Society 16 , On manifolds supporting distributionally uniquely ergodic diffeomorphisms.
Dynamics on the Riemann Sphere: A Bodil Branner Festschrift | Mathematical Association of America
Avila, B. Fayad, A.
Journal of Differential Geometry 99 , Journal of the American Mathematical Society 28 , Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows. Viana, A. Journal of the European Mathematical Society 17 , The visits to zero of a random walk driven by an irrational rotation. Monotonic cocycles.
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Some functional equations connected with the iteration of rational functions Russian. In: Algebra i Analiz 1 , translation in Leningrad Math. Google Scholar. Eremenko A. Fatou P.
Julia G. Lectures on the icosahedron and the solution of equations of the fifth degree. Dover Publications, Inc. Inou H. McMullen C. Medvedev and T. Invariant varieties for polynomial dynamical systems. Annals of Mathematics 1 , 81— Google Scholar. Dynamics in one complex variable. Open quantum systems; Appendices; References. The basic properties of solitons are introduced here using examples from macroscopic physics e.
Publications and Preprints
The book then presents the main theoretical methods before discussing applications from solid state or atomic physics such as dislocations, excitations in spin chains, conducting polymers, ferroelectrics and Bose-Einstein condensates. Examples are also taken from biological physics and include energy transfer in proteins and DNA fluctuations.
Throughout the book the authors emphasize a new approach to modelling nonlinearities in physics. Instead of a perturbative approach, nonlinearities are treated intrinsically and the analysis based on the soliton equations introduced in this book. Based on the authors' graduate course, this textbook gives an instructive view of the physics of solitons for students with a basic knowledge of general physics, and classical and quantum mechanics.
Different Classes of Solitons: 1. The Korteweg-de Vries equation; 2. Sine-Gordon equation; 3. The nonlinear Schrodinger equation; 4. Modelling: waves in a plasma; Part II. Mathematical Methods for the Study of Solitons: 5. Linearisation around a soliton; 6. Collective-coordinate method; 7. The inverse-scattering transform; Part III. Examples in Solid State and Atomic Physics: 8.
The Fermi-Pasta-Ulam problem; 9. A simple model for dislocations; Ferroelectric domain walls; Incommensurate phases; Solitons in magnetic systems;