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| Author | : Hendrik W. Broer |
| Publisher | : Springer |
| Total Pages | : 203 |
| Release | : 2009-01-25 |
| Genre | : Mathematics |
| ISBN | : 3540496130 |
Download Quasi-Periodic Motions in Families of Dynamical Systems Book in PDF, ePub and Kindle
This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.
| Author | : Hendrik W. Broer |
| Publisher | : |
| Total Pages | : 216 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662167953 |
Download Quasi-Periodic Motions in Families of Dynamical Systems Book in PDF, ePub and Kindle
| Author | : Jurgen Moser |
| Publisher | : Princeton University Press |
| Total Pages | : 216 |
| Release | : 2016-03-02 |
| Genre | : Science |
| ISBN | : 1400882699 |
Download Stable and Random Motions in Dynamical Systems Book in PDF, ePub and Kindle
For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.
| Author | : H.W Broer |
| Publisher | : CRC Press |
| Total Pages | : 498 |
| Release | : 2001-06-18 |
| Genre | : Mathematics |
| ISBN | : 9781420034288 |
Download Global Analysis of Dynamical Systems Book in PDF, ePub and Kindle
Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
| Author | : H. Broer |
| Publisher | : Elsevier |
| Total Pages | : 556 |
| Release | : 2010-11-10 |
| Genre | : Mathematics |
| ISBN | : 0080932266 |
Download Handbook of Dynamical Systems Book in PDF, ePub and Kindle
In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
| Author | : Andreas Johann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 628 |
| Release | : 2013-09-24 |
| Genre | : Mathematics |
| ISBN | : 3034804512 |
Download Recent Trends in Dynamical Systems Book in PDF, ePub and Kindle
This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.
| Author | : Heinz Hanßmann |
| Publisher | : Springer |
| Total Pages | : 248 |
| Release | : 2006-10-18 |
| Genre | : Mathematics |
| ISBN | : 3540388966 |
Download Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems Book in PDF, ePub and Kindle
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
| Author | : Hakan Eliasson |
| Publisher | : Springer |
| Total Pages | : 207 |
| Release | : 2004-10-11 |
| Genre | : Mathematics |
| ISBN | : 3540479287 |
Download Dynamical Systems and Small Divisors Book in PDF, ePub and Kindle
Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included.
| Author | : Carles Casacuberta |
| Publisher | : Birkhäuser |
| Total Pages | : 630 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034882661 |
Download European Congress of Mathematics Book in PDF, ePub and Kindle
This is the second volume of the proceedings of the third 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 as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. 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.
| Author | : Yunping Jiang |
| Publisher | : World Scientific |
| Total Pages | : 372 |
| Release | : 1999-12-16 |
| Genre | : |
| ISBN | : 9814543276 |
Download Dynamical Systems Book in PDF, ePub and Kindle
This volume constitutes the proceedings of the International Conference on Dynamical Systems in Honor of Prof. Liao Shantao (1920–97). The Third World Academy of Sciences awarded the first ever mathematics prize in 1985 to Prof. Liao in recognition of his foundational work in differentiable dynamical systems and his work in periodic transformation of spheres. The conference was held in Beijing in August 1998. There were about 90 participants, and nearly 60 talks were delivered. The topics covered include differentiable dynamics, topological dynamics, hamiltonian dynamics, complex dynamics, ergodic and stochastic dynamics, and fractals theory. Dynamical systems is a field with many difficult problems, and techniques are being developed to deal with those problems. This volume contains original studies of great mathematical depth and presents some of the fascinating numerical experiments. Contents: The Dynamics of the Henon-Like Maps (Y-L Cao)Nonchaos for Substitution Minimal Systems (Q-J Fan et al.)A Note on the Obstruction Sets of Discrete Systems (S-B Gan)Topological Pressure of Continuous Flows Without Fixed Points (L-F He et al.)Nonlinearity, Quasisymmetry, Differentiability, and Rigidity in One-Dimensional Dynamics (Y-P Jiang)The Stability of the Equilibrium of Planar Hamiltonian Systems (B Liu)Existence and Uniqueness of Analytic Solutions of Iterative Functional Equations (J-H Mai & X-H Liu)On Bimodal Collet-Eckmann Maps (L-Y Wang)An Introduction to the C1 Connecting Lemma (L Wen)Partial Entropy, Bundle-Like Entropy and Topological Entropy (F-P Zeng)and other papers Readership: Research mathematicians and graduates in analysis and differential equations. Keywords:Dynamical Systems;Periodic Transformation;Topological Dynamics;Hamiltonian Dynamics;Complex Dynamics;Ergodic;Stochastic Dynamics;Fractals Theory;Henon-Like Maps;Fixed Points;Nonlinearity;Quasisymmetry;Planar Hamiltonian Systems;Analytic Solutions;Iterative Functional Equations;Partial Entropy;Bundle-Like Entropy;Topological Entropy
