Download or read book Iterated Maps on the Interval as Dynamical Systems written by Pierre Collet and published by Springer Science & Business Media. This book was released on 2009-08-25 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. Iterated Maps on the Interval as Dynamical Systems is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems .

Download or read book Iterated Maps on the Interval as Dynamical Systems written by Pierre Collet and published by . This book was released on 1986 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Iterated Maps of the Interval written by John Willard Milnor and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterates of Maps on an Interval written by C. Preston and published by Springer. This book was released on 2006-11-15 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterated Maps of the Interval and the Influence of Noise written by and published by . This book was released on 1990 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterates of Maps on an Interval written by Chris Preston and published by . This book was released on 1983 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Superstable Parameters for Iterated Maps of an Interval written by Lennart Falk and published by . This book was released on 1989 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterates of Maps on an Interval written by Sivalingam Sivanesan and published by . This book was released on 1990 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterates of Piecewise Monotone Mappings on an Interval written by Chris Preston and published by Springer. This book was released on 2006-11-15 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.

Download or read book Iterates of maps on an interval written by Christopher J. Preston and published by . This book was released on 1982 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterated Function Systems of Interval Maps written by Masoumeh Gharaei and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This thesis contains three related articles which are inserted in separate chapters. The chapters are self contained, hence it is possible to read each of them independently. In each of the chapters we discuss iterated function systems, IFSs, generated by finitely many continuous maps f1, . . . , fk on the unit interval I = [0, 1], taken with positive probabilities pi, ∑ki=1 pi =1, randomly at each iterate. We always assume that these maps fix the boundaries of the interval I and study dynamics of the system under some conditions like the sign of the Lyapunov exponent at the boundaries of the interval. The sign of Lyapunov exponent at a boundary determines whether the boundary is, on average, attracting (negative Lyapunov exponent), neutral (zero), or repelling (positive). We discuss occurrence of intriguing dynamical phenomena such as synchronization, intermingled basins and intermittency, in this context."--Samenvatting auteur.

Download or read book Geometric Pressure for Multimodal Maps of the Interval written by Feliks Przytycki and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. The authors work in a setting of generalized multimodal maps, that is, smooth maps f of a finite union of compact intervals Iˆ in R into R with non-flat critical points, such that on its maximal forward invariant set K the map f is topologically transitive and has positive topological entropy. They prove that several notions of non-uniform hyperbolicity of f|K are equivalent (including uniform hyperbolicity on periodic orbits, TCE & all periodic orbits in K hyperbolic repelling, Lyapunov hyperbolicity, and exponential shrinking of pull-backs). They prove that several definitions of geometric pressure P(t), that is pressure for the map f|K and the potential −tlog|f′|, give the same value (including pressure on periodic orbits, “tree” pressure, variational pressures and conformal pressure). Finally they prove that, provided all periodic orbits in K are hyperbolic repelling, the function P(t) is real analytic for t between the “condensation” and “freezing” parameters and that for each such t there exists unique equilibrium (and conformal) measure satisfying strong statistical properties.

Download or read book Collected Papers of John Milnor written by John Willard Milnor and published by American Mathematical Soc.. This book was released on 1994 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book European Congress of Mathematics written by Antal Balog and published by Birkhäuser. This book was released on 2012-12-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua.

Download or read book Concepts and Results in Chaotic Dynamics A Short Course written by Pierre Collet and published by Springer Science & Business Media. This book was released on 2007-07-07 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.

Download or read book Global Theory of Dynamical Systems written by Z. Nitecki and published by Springer. This book was released on 2006-11-14 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete Dynamics And Difference Equations Proceedings Of The Twelfth International Conference On Difference Equations And Applications written by Saber N Elaydi and published by World Scientific. This book was released on 2010-11-02 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal.The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.