Download or read book Dynamics of Transcendental Entire Functions with Escaping Singular Orbits written by Leticia Pardo Simón and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinite dimensional Thurston Theory and Transcendental Dynamics with Escaping Singular Orbits written by Konstantin Bogdanov and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this thesis is to distinguish and classify a family of transcendental entire functions in terms of the dynamics of their singular values. This classification follows the lead of Thurston's famous characterization theorem of rational maps, but in the context of transcendental mappings, and works with infinite rather than finite dimensional Teichmüller theory.The families of maps that we investigate are compositions of exponential and polynomial functions, and we focus on the case where all singular values converge (fast) to infinity: this is in analogy to quadratic polynomials where the set of functions with singular values converging to infinity forms the complement of the celebrated Mandelbrot set. Even for polynomials, the situation becomes far more challenging when there is more than one singular value, as each singular value introduces another degree of freedom. In the transcendental case, the description of individual escaping singular values introduces additional challenges that have been understood only recently, and a classification of such maps is known so far only for the family of exponential maps.The construction of an entire transcendental function with prescribed speed of escape and combinatorics of singular values involves consideration of iterates of a map (in analogy to Thurston's sigma-mapping) that acts on an infinite-dimensional Teichmüller space (more precisely, Teichmüller space modeled on the complement of singular orbits).
Download or read book Transcendental Dynamics and Complex Analysis written by Philip J. Rippon and published by Cambridge University Press. This book was released on 2008-06-26 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting papers by researchers in transcendental dynamics and complex analysis, this exciting new and modern book is written in honor of Noel Baker, who laid the foundations of transcendental complex dynamics. The papers describe the state of the art in this subject, with new results on completely invariant domains, wandering domains, the exponential parameter space, and normal families. The inclusion of comprehensive survey articles on dimensions of Julia sets, buried components of Julia sets, Baker domains, Fatou components of functions of small growth, and ergodic theory of transcendental meromorphic functions means this is essential reading for students and researchers in complex dynamics and complex analysis.
Download or read book Holomorphic Dynamical Systems written by Nessim Sibony and published by Springer Science & Business Media. This book was released on 2010-07-31 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.
Download or read book Early Days in Complex Dynamics written by Daniel S. Alexander and published by American Mathematical Soc.. This book was released on 2012 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.
Download or read book Topological Dynamics of Transcendental Entire Functions written by Helena Mihaljevic-Brandt and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamics of Transcendental Entire Functions written by Xiaoling Wang and published by . This book was released on 2003 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Holomorphic Dynamics written by S. Morosawa and published by Cambridge University Press. This book was released on 2000-01-13 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, is a comprehensive introduction to holomorphic dynamics, that is the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.
Download or read book On the Dynamical Fine Structure of Entire Transcendental Functions written by Günter Rottenfusser and published by . This book was released on 2005 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we give several answers to questions of Fatou and Eremenko. For a large class of transcendental entire functions we show that all components of the set of escaping points are path connected. In particular we show that for all bounded type functions of finite order and their finite compositions, the set of escaping points is organized in terms of dynamic rays. Ruthermore we show that, in logarithmic coordinates, the strong version of Eremenko's conjecture is false. That is, there exists a function F such that the according set of escaping points contains a point which can not be connected to infinity by a curve contained in the escaping set. For the example of the family of cosine functions a exp(z)+b exp(-z) we give an explicit parameterization of the dynamic rays. We also describe the dimension paradox: the set of escaping points on rays has Hausdorff dimension 1, while the set of escaping landing points has Hausdorff dimension 2 and even positive planar Lebesgue measure.
Download or read book Holomorphic Dynamics and Renormalization written by Mikhail Lyubich and published by American Mathematical Soc.. This book was released on 2008 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collects papers that reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. This title contains papers that introduces the reader to this fascinating world and a related area of transcendental dynamics. It also includes open problems and computer simulations.
Download or read book Quasiconformal Surgery in Holomorphic Dynamics written by Bodil Branner and published by Cambridge University Press. This book was released on 2014-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Analysis and Applications written by A. P. Dwivedi and published by . This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers presented at the 7th Annual Conference of Vijnana Parishad of India, organised at the Dept. of Mathematics, HBTI, Kanpur, on October 24-26, 1997.
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Download or read book Nonlinearity written by and published by . This book was released on 2008 with total page 1104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research Problems in Function Theory written by Walter K. Hayman and published by Springer Nature. This book was released on 2019-09-07 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1967 Walter K. Hayman published ‘Research Problems in Function Theory’, a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as ‘Hayman's List’. This Fiftieth Anniversary Edition contains the complete ‘Hayman's List’ for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems and results needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.
Download or read book Fundamentals of Astrodynamics written by Roger R. Bate and published by Courier Corporation. This book was released on 1971-01-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching text developed by U.S. Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body and n-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.
