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Titlebook: Nonlinear Dynamical Systems and Chaos; H. W. Broer,S. A. Gils,F. Takens Conference proceedings 1996 Springer Basel AG 1996 KAM theory.bifu

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书目名称Nonlinear Dynamical Systems and Chaos
编辑H. W. Broer,S. A. Gils,F. Takens
视频video
概述The book can be recommended to researchers specializing in dynamical systems." - Applied Mathematics, XL
丛书名称Progress in Nonlinear Differential Equations and Their Applications
图书封面Titlebook: Nonlinear Dynamical Systems and Chaos;  H. W. Broer,S. A. Gils,F. Takens Conference proceedings 1996 Springer Basel AG 1996 KAM theory.bifu
描述Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
出版日期Conference proceedings 1996
关键词KAM theory; bifurcation; chaos; dynamical systems; time series analysis
版次1
doihttps://doi.org/10.1007/978-3-0348-7518-9
isbn_softcover978-3-0348-7520-2
isbn_ebook978-3-0348-7518-9Series ISSN 1421-1750 Series E-ISSN 2374-0280
issn_series 1421-1750
copyrightSpringer Basel AG 1996
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The Rolling Discerpendicular to the disc, one can reduce the dynamics to a four dimensional system, see section 2. This reduced system was obtained for the first time by Ferrers [6] in 1872, using Euler-angles. The first serious analysis of these equations was given by Vierkandt [18] in 1892. He showed that almost all orbits are periodic.
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Testing for ,,-Symmetry with a Recursive Detectivemoreover the numerical evaluation can be costly. Representation theory and invariant theory are used to derive efficient methods. A method is proposed to evaluate a detective recursively for the symmetric group .. Comparision shows that this is very efficient both in CPU time and in storage.
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Parametric and autoparametric resonancemetrically excited system in section 2. This system is a dissipative version of the study by Broer and Vegter (1992). In section 3 we consider an autoparametric two degrees of freedom system which is in some sense a generalisation of section 2. Such a system admits a richer bifurcation structure and chaotic dynamics.
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Towards a Global Theory of Singularly Perturbed Dynamical Systemslocal theory to a description of qualitative features of the global dynamics for systems with two time scales. We fill in portions of this outline within the context of systems that have two slow variables and two fast variables. Even within this low dimensional setting, most basic questions about global properties remain unanswered.
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Conference proceedings 1996er of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
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