Meromorphic Dynamics Volume 1
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Meromorphic Dynamics Volume 1
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Author : Janina Kotus
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-04
Meromorphic Dynamics Volume 1 written by Janina Kotus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-04 with Mathematics categories.
This text, the first of two volumes, provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various kinds of conformal measures, conformal graph directed Markov systems and iterated functions systems, semi-local dynamics of analytic functions, and nice sets. Many examples are included, along with detailed explanations of essential concepts and full proofs, in what is sure to be an indispensable reference for both researchers and graduate students.
Meromorphic Dynamics Volume 2
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Author : Janina Kotus
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-04
Meromorphic Dynamics Volume 2 written by Janina Kotus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-04 with Mathematics categories.
This text, the second of two volumes, builds on the foundational material on ergodic theory and geometric measure theory provided in Volume I, and applies all the techniques discussed to describe the beautiful and rich dynamics of elliptic functions. The text begins with an introduction to topological dynamics of transcendental meromorphic functions, before progressing to elliptic functions, discussing at length their classical properties, measurable dynamics and fractal geometry. The authors then look in depth at compactly non-recurrent elliptic functions. Much of this material is appearing for the first time in book or paper form. Both senior and junior researchers working in ergodic theory and dynamical systems will appreciate what is sure to be an indispensable reference.
Holomorphic Dynamical Systems
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Author : Nessim Sibony
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-31
Holomorphic Dynamical Systems written by Nessim Sibony and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-31 with Mathematics categories.
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.
Uniqueness Theory Of Meromorphic Functions
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Author : Chung-Chun Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-10-04
Uniqueness Theory Of Meromorphic Functions written by Chung-Chun Yang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-04 with Mathematics categories.
This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Developed by R. Nevanlinna, a Finnish mathematician, early in the 1920's, research in the field has developed rapidly over the past three decades with a great deal of fruitful results. This book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results. In addition, useful skills and simple proofs are introduced. This book is suitable for higher level and graduate students who have a basic grounding in complex analysis, but will also appeal to researchers in mathematics.
Classical Complex Analysis A Geometric Approach Volume 1
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Author : I-hsiung Lin
language : en
Publisher: World Scientific Publishing Company
Release Date : 2010-09-09
Classical Complex Analysis A Geometric Approach Volume 1 written by I-hsiung Lin and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Mathematics categories.
Classical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 1 begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described in detail, and various applications of residues are included; analytic continuation is also introduced.The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.
Meromorphic Dynamics
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Author : Janina Kotus
language : en
Publisher: Cambridge University Press
Release Date : 2023
Meromorphic Dynamics written by Janina Kotus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Functions, Meromorphic categories.
"The first of two volumes provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various kinds of conformal measures, conformal graph directed Markov systems and iterated functions systems, semi-local dynamics of analytic functions, and nice sets. Many examples are included, along with detailed explanations of essential concepts and full proofs, in what is sure to be an indispensable reference for both researchers and graduate students"--
Dynamical Systems And Random Processes
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Author : Jane Hawkins
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-23
Dynamical Systems And Random Processes written by Jane Hawkins and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-23 with Mathematics categories.
This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13–15, 2018, at Agnes Scott College, Decatur, Georgia. The papers cover various topics in dynamics and randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages. The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.
Complex Dynamics And Geometry
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Author : Dominique Cerveau
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Complex Dynamics And Geometry written by Dominique Cerveau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, ``Etat de la recherche'', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points. E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the ``Etat de la recherche de la SMF'' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.
An Introduction To Symbolic Dynamics And Coding
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Author : Douglas Lind
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-24
An Introduction To Symbolic Dynamics And Coding written by Douglas Lind and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-24 with Computers categories.
This first textbook on this important subject is suitable for both engineering and mathematics students.
Soliton Equations And Their Algebro Geometric Solutions Volume 1 1 1 Dimensional Continuous Models
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Author : Fritz Gesztesy
language : en
Publisher: Cambridge University Press
Release Date : 2003-06-05
Soliton Equations And Their Algebro Geometric Solutions Volume 1 1 1 Dimensional Continuous Models written by Fritz Gesztesy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-05 with Mathematics categories.
The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text.