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Author: Ludwig Reich
Publisher:
ISBN:
Category :
Languages : de
Pages : 261
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Author: Ludwig Reich
Publisher:
ISBN:
Category :
Languages : de
Pages : 261
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Book Description
Author: Ludwig Reich
Publisher:
ISBN:
Category : Iterative methods (Mathematics)
Languages : en
Pages : 261
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Book Description
Author: W Forg-rob
Publisher: World Scientific
ISBN: 9814547891
Category :
Languages : en
Pages : 298
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Book Description
Iteration theory has its roots in the operation of substituting functions into itself. This has led to questions like that of the behaviour of functions by repeating this substitution and when the number of iterations tends to infinity. The terms 'orbit' and 'chaos' appropriately describe this behaviour. Dynamical systems and the theory of functional equations play important roles in this field.
Author: J P Lampreia
Publisher: World Scientific
ISBN: 9814554340
Category :
Languages : en
Pages : 374
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Book Description
The main theme of the ECIT conferences is Iteration Theory, on the borderline between Dynamics and Functional Equations. The aim is to foster symbiosis between mainstream dynamics and iteration theory treated in the style of functional equations theory. The following topics are focused: turbulence and iteration, characterization of chaos, kneading theory, symbolic dynamics, bifurcation, periods of maps, topological dynamics, discrete retarded dynamical systems, cellular automata as dynamical systems, iterative roots of formal power series, iterative roots of polynomials, phantom iterative roots, iterative groups and semigroups, families of commuting functions, algebraic aspects of iteration theory and functional equations.
Author:
Publisher:
ISBN:
Category : Iterative methods (Mathematics)
Languages : en
Pages : 256
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Author: Luis Alseda
Publisher: World Scientific Publishing Company
ISBN: 9813105593
Category : Science
Languages : en
Pages : 433
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Book Description
This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of “chaos” present in it; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself.
Author: Matthias Aschenbrenner
Publisher: Princeton University Press
ISBN: 0691175438
Category : Mathematics
Languages : en
Pages : 873
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Book Description
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Author: Lakshmi Burra
Publisher: Springer
ISBN: 8132220927
Category : Mathematics
Languages : en
Pages : 118
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Book Description
Using phase–plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems, complex behavior in a map can be indicated by showing the existence of a Smale-horseshoe-like structure, either for the map itself or its iterates. This usually requires some assumptions about the map, such as a diffeomorphism and some hyperbolicity conditions. In this text, less stringent definitions of a horseshoe have been suggested so as to reproduce some geometrical features typical of the Smale horseshoe, while leaving out the hyperbolicity conditions associated with it. This leads to the study of the so-called topological horseshoes. The presence of chaos-like dynamics in a vertically driven planar pendulum, a pendulum of variable length, and in other more general related equations is also proved.
Author: Tanja Eisner
Publisher: Springer
ISBN: 3319168983
Category : Mathematics
Languages : en
Pages : 630
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Book Description
Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory
Author: Christian Mira
Publisher:
ISBN:
Category :
Languages : en
Pages : 359
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Book Description
