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Iterated maps on the interval as dynamical systems
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Pierre Collet, Jean-Pierre Eckmann
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a ...
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Complex Dynamics
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Lennart Carleson, Theodore W Gamelin
Complex Dynamics discusses the properties of conformal mappings in the complex plane, a subject that is closely connected to the study of fractals and chaos. Indeed the culmination of the book is a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. The book focuses on the analytic side of this ...
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The Real Fatou Conjecture. (Am-144)
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Jacek Graczyk, Grzegorz Swiatek
In 1920, Pierre Fatou expressed the conjecture that - except for special cases - all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set ...
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Mappings of Operator Algebras
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Huzihiro Araki, R V Kadison
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An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces
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David Jackson, Terry I Visentin
Maps are beguilingly simple structures with deep and ubiquitous properties. They arise in an essential way in many areas of mathematics and mathematical physics, but require considerable time and computational effort to generate. Few collected drawings are available for reference, and little has been written, in book form, about their enumerative ...
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Similarity Problems and Completely Bounded Maps
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Gilles Pisier
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the ...
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Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos
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McCauley
This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical ...
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Universal Spaces and Mappings
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S D Iliadis
The book is devoted to universality problems. A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as: universal mappings, dimension theory, action of groups, inverse spectra, isometrical ...
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99 Points of Intersection: Examples-Pictures-Proofs
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Hans Walser, Jean J Pedersen (Editor), William Watkins (Editor)
The 99 points of intersection presented here were collected during a year-long search for surprising concurrence of lines. For each example we find compelling evidence for the sometimes startling fact that in a geometric figure three straight lines, or sometimes circles, pass through one and the same point. Of course, we are familiar with some ...
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Fixed Point Theory and Applications
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Ravi P Agarwal, Maria Meehan, Donal O'Regan
This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. ...
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Isovector Methods for Equations of Balance, with Programs for Computer Assistance in Operator Calculations and an Exposition of Practical Topics of the Exterior Calculus
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Dominic G B Edelen
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Iteration of Rational Functions
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Alan F Beardon
This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sullivan and Shishikura. Many of the details of the ...
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The Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids
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Rob Sturman, Julio M Ottino, Stephen Wiggins
Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them Are there tools that allow for prediction and quantification The authors show ...
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Symbolic Dynamics of Trapezoidal Maps
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James D Louck, N Metropolis
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Analysis and Modelling of Discrete Dynamical Systems
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Daniel Benest (Editor), Claude Froeschle (Editor)
The theory of dynamical systems, or mappings, plays an important role in various disciplines of modern physics, including celestial mechanics and fluid mechanics. This comprehensive introduction to the general study of mappings has particular emphasis on their applications to the dynamics of the solar system. The book forms a bridge between ...
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Completely Bounded Maps and Operator Algebras
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by
Vern I Paulsen
In this book the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and ...
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Approximation-Solvability of Nonlinear Functional and Differential Equations
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Wolodymyr V Petryshyn, Petryshyn V Petryshyn
This reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications. ...
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Construction of Mappings for Hamiltonian Systems and Their Applications
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Sadrilla S Abdullaev
Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, ...
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Probabilistic Methods in Discrete Mathematics, Volume 5 Probabilistic Methods in Discrete Mathematics: Proceedings of the Fifth International Petrozavodsk Conference, Petrozavodsk, Russia, June 1-6, 2000
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by
V F Kolchin, V YA Kozlov (Editor), V V Mazalov (Editor)
This volume of proceedings contains the plenary lectures and selected contributed papers which were given at the Fifth International Petrozavodsk Conference on Probabilistic Methods in Discrete Mathematics, 1-6 June 2000, Petrozavodsk, Russia. The themes of the conference covered almost all areas of discrete mathematics, such as probabilistic ...
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Stochasticity and Partial Order
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Peter M Alberti, A Uhlmann
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Recurrence in Topological Dynamics
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Ethan Akin
This groundbreaking volume is the first to elaborate the theory of set families as a tool for studying the phenomenon of recurrence. The theory is implicit in such seminal works as Hillel Furstenberg's "Recurrence in Ergodic Theory and Combinational Number Theory", but Ethan Akin's study elaborates it in detail, defining such elements of theory as ...
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General Topology II: Compactness, Homologies of General Spaces
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A V Arhangel'skii (Editor), A V Arkhangel'skifi, J M Lysko (Translator)
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From Quantum Cohomology to Integrable Systems
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Martin A Guest
Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such ...
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On Global Univalence Theorems
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T Parthasarathy
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Dynamics of One-Dimensional Maps
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A N Sharkovsky, S F Kolyada, A G Sivak
The theory of one-dimensional systems is one of the most efficient tools of nonlinear dynamics, as, on the one hand, it describes one-dimensional systems fairly completely, and on the other hand exhibits all basic complicated nonlinear effects. This volume has two main goals. Firstly, it acquaints the reader with the fundamentals of the theory of ...
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