Six Lectures On Dynamical Systems
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Author | : Bernd Aulbach |
Publisher | : World Scientific |
Total Pages | : 332 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9789810225483 |
Download Six Lectures on Dynamical Systems Book in PDF, Epub and Kindle
This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included.The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level.
Author | : Bernd Aulbach |
Publisher | : World Scientific |
Total Pages | : 323 |
Release | : 1996-05-15 |
Genre | : Mathematics |
ISBN | : 9814499420 |
Download Six Lectures On Dynamical Systems Book in PDF, Epub and Kindle
This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included.The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level.
Author | : Ludwig Arnold |
Publisher | : |
Total Pages | : 44 |
Release | : 1994 |
Genre | : |
ISBN | : |
Download Six Lectures on Random Dynamical Systems Book in PDF, Epub and Kindle
Author | : Eduard Zehnder |
Publisher | : European Mathematical Society |
Total Pages | : 372 |
Release | : 2010 |
Genre | : Dynamics |
ISBN | : 9783037190814 |
Download Lectures on Dynamical Systems Book in PDF, Epub and Kindle
This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.
Author | : Kotik K. Lee |
Publisher | : World Scientific |
Total Pages | : 476 |
Release | : 1992 |
Genre | : Science |
ISBN | : 9789971509651 |
Download Lectures on Dynamical Systems, Structural Stability, and Their Applications Book in PDF, Epub and Kindle
The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Author | : C. Marchioro |
Publisher | : Springer Science & Business Media |
Total Pages | : 312 |
Release | : 2011-06-10 |
Genre | : Mathematics |
ISBN | : 3642139299 |
Download Dynamical Systems Book in PDF, Epub and Kindle
Lectures: J. Guckenheimer: Bifurcations of dynamical systems.- J. Moser: Various aspects of integrable.- S. Newhouse: Lectures on dynamical systems.- Seminars: A. Chenciner: Hopf bifurcation for invariant tori.- M. Misiurewicz: Horseshoes for continuous mappings of an interval.
Author | : Peter E. Kloeden |
Publisher | : American Mathematical Soc. |
Total Pages | : 274 |
Release | : 2011-08-17 |
Genre | : Mathematics |
ISBN | : 0821868713 |
Download Nonautonomous Dynamical Systems Book in PDF, Epub and Kindle
The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.
Author | : Peter E. Kloeden |
Publisher | : Springer |
Total Pages | : 326 |
Release | : 2014-01-22 |
Genre | : Mathematics |
ISBN | : 3319030809 |
Download Nonautonomous Dynamical Systems in the Life Sciences Book in PDF, Epub and Kindle
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Author | : K.J. Palmer |
Publisher | : Springer Science & Business Media |
Total Pages | : 307 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475732104 |
Download Shadowing in Dynamical Systems Book in PDF, Epub and Kindle
In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.
Author | : Ludwig Arnold |
Publisher | : Springer Science & Business Media |
Total Pages | : 590 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662128780 |
Download Random Dynamical Systems Book in PDF, Epub and Kindle
The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.