Author : Hendrik Wolter Broer
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 41,65 MB
Release : 1990
Category : Mathematics
ISBN : 082182483X
Part I. We consider dynamical systems depending on parameters in various, both conservative and dissipative settings. For such systems integrability is defined as equivariance with respect to an appropriate torus action.
Author : Gregorius Bonifatius Huitema
Publisher :
Page : 112 pages
File Size : 40,61 MB
Release : 1988
Category : Differentiable mappings
ISBN :
Author : Gregorius B. Huitema
Publisher :
Page : 112 pages
File Size : 46,4 MB
Release : 1988
Category :
ISBN :
Author : H. W. Broer
Publisher :
Page : 17 pages
File Size : 50,40 MB
Release : 1993
Category :
ISBN :
Author : H. W. Broer
Publisher :
Page : 76 pages
File Size : 15,64 MB
Release : 1987
Category :
ISBN :
Author : Hendrik W. Broer
Publisher : Springer
Page : 203 pages
File Size : 26,20 MB
Release : 2009-01-25
Category : Mathematics
ISBN : 3540496130
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 :
Publisher :
Page : 964 pages
File Size : 40,12 MB
Release : 1988
Category : Aeronautics
ISBN :
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author : Christos H. Skiadas
Publisher : CRC Press
Page : 921 pages
File Size : 25,9 MB
Release : 2017-12-19
Category : Mathematics
ISBN : 1315356546
In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
Author : Giuseppe Gaeta
Publisher : World Scientific
Page : 311 pages
File Size : 31,89 MB
Release : 2007
Category : Mathematics
ISBN : 9812776168
This proceedings volume is devoted to the interplay of symmetry and perturbation theory, as well as to cognate fields such as integrable systems, normal forms, n-body dynamics and choreographies, geometry and symmetry of differential equations, and finite and infinite dimensional dynamical systems. The papers collected here provide an up-to-date overview of the research in the field, and have many leading scientists in the field among their authors, including: D Alekseevsky, S Benenti, H Broer, A Degasperis, M E Fels, T Gramchev, H Hanssmann, J Krashil'shchik, B Kruglikov, D Krupka, O Krupkova, S Lombardo, P Morando, O Morozov, N N Nekhoroshev, F Oliveri, P J Olver, J A Sanders, M A Teixeira, S Terracini, F Verhulst, P Winternitz, B Zhilinskii.
Author : William F. Langford
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 40,22 MB
Release : 1995-01-01
Category : Mathematics
ISBN : 9780821885871
This volume presents new research on normal forms, symmetry, homoclinic cycles, and chaos, from the Workshop on Normal Forms and Homoclinic Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in November 1992, in Waterloo, Canada. The workshop bridged the local and global analysis of dynamical systems with emphasis on normal forms and the recently discovered homoclinic cycles which may arise in normal forms. Specific topics covered in this volume include normal forms for dissipative, conservative, and reversible vector fields, and for symplectic maps; the effects of symmetry on normal forms; the persistence of homoclinic cycles; symmetry-breaking, both spontaneous and induced; mode interactions; resonances; intermittency; numerical computation of orbits in phase space; applications to flow-induced vibrations and to mechanical and structural systems; general methods for calculation of normal forms; and chaotic dynamics arising from normal forms. Of the 32 presentations given at this workshop, 14 of them are represented by papers in this volume.
