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Tuesday, April 28, 2020 | History

7 edition of Bifurcations in Hamiltonian systems found in the catalog.

Bifurcations in Hamiltonian systems

computing singularities by Gröbner bases

by

  • 240 Want to read
  • 2 Currently reading

Published by Springer-Verlag in New York .
Written in English

    Subjects:
  • Hamiltonian systems,
  • Bifurcation theory,
  • Singularities (Mathematics),
  • Gröbner bases

  • Edition Notes

    Includes bibliographical references and index.

    StatementHenk Broer ... [et al.].
    SeriesLecture notes in mathematics -- 1806., Lecture notes in mathematics (Springer-Verlag) -- 1806.
    ContributionsBroer, H. W. 1950-
    Classifications
    LC ClassificationsQA3 .L28 no. 1806, QA614.83 .L28 no. 1806
    The Physical Object
    Paginationxiii, 169 p. :
    Number of Pages169
    ID Numbers
    Open LibraryOL17720644M
    ISBN 103540004033
    LC Control Number2003041220

    systems, Hamiltonian systems, dynamics on networks, in nite dimensional systems (partial di erential equations, delay di erential equations) and random dynamical systems (stochastic di erential equations). The term bifurcation was originally used by Poincar e to describe the splitting of equilibria in a family of di erential Size: 3MB.


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Bifurcations in Hamiltonian systems Download PDF EPUB FB2

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to. Buy Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems: Results and Examples (Lecture Notes in Mathematics) on FREE SHIPPING on qualified ordersCited by: The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems.

They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear. Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems: Results and Examples (Lecture Notes in Mathematics Book ) - Kindle edition by Heinz Hanßmann.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems: Results and.

"This book deals with bifurcations of invariant tori in Hamiltonian systems, in particular in near-integrable systems. The book closes with a series of appendices, in which technical or more fundamental details are summarised.

This well-written monograph represents a welcome contribution to the literature in this field—I am not aware Brand: Springer-Verlag Berlin Heidelberg.

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. The volume focuses on two such reduction methods, the planar reduction Read more. The purpose of the present chapter is once again to show on concrete new examples that chaos in one-dimensional unimodal mappings, dynamical chaos in systems of ordinary differential equations, diffusion chaos in systems of the equations with partial derivatives and chaos in Hamiltonian and conservative systems are generated by cascades of bifurcations under universal bifurcation Feigenbaum Cited by: 1.

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems.

While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameterwithout the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system.

Systems’. On Lyapunov exponents, we include some notes from Allesandro Morbidelli’s book ‘Modern Celestial Mechanics, Aspects of Solar System Dynamics.’ In future I would like to add more examples from the book called Bifurcations in Hamiltonian systems (Broer et File Size: 1MB.

Umbilical torus bifurcations in Hamiltonian systems Article in Journal of Differential Equations (1) March with 41 Reads How we measure 'reads'. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation.

The main topics include Hopf bifurcation of limit cycles from a center or a focus, homoclinic bifurcations near a homoclinic or a heteroclinic loop, and the number of limit cycles in global bifurcations of near-Hamiltonian polynomial systems of arbitrary degree.

This book will be of use to graduate mathematics students as well as scientists. We introduce a new class of billiards—billiard books, which are integrable Hamiltonian systems.

It turns out that for any nondegenerate three-dimensional bifurcation (3-atom), a billiard book can be algorithmically constructed in which such a bifurcation appears. Consequently, any integrable Hamiltonian nondegenerate dynamical system with two degrees of freedom can be modelled in some Cited by: 3.

Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems Article (PDF Available) in Science Advances 5(4):eaav April with 1, Reads.

The generic bifurcations are useful to hydrodynamics and are also relevant to the analysis of dissipative physical systems. The bifurcations of Hamiltonian dynamical systems are special in character.

The analysis of bifurcations characterizes the local recurrent points. The study of bifurcations of a periodic orbit presents no new problems. Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems.

This book presents a detailed analysis of bifurcation and chaos in simple non-linear systems, based on previous works of the author. Practical examples for mechanical and biomechanical systems are discussed.

The use of both numerical and analytical approaches allows for a deeper insight into non-linear dynamical phenomena. Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics.

The Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems, Richard Cushman, Johnathan Robbins and Dimitrii. Download Bifurcations In Hamiltonian Systems: Computing Singularities By Gröbner Bases The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems.

The locally Hamiltonian KAM Theory was constructed by I.O. Parasyuk and Yu.V. Loveĭkin, see their papers concerning coisotropic [,–] and atropic [] tori in locally Hamiltonian systems.

This theory has been briefly reviewed in []. By the way, Lemma 20 is valid for invariant tori of locally Hamiltonian systems as well. Classical Mechanics and Dynamical Systems. This note explains the following topics: Classical mechanics, Lagrange equations, Hamilton’s equations, Variational principle, Hamilton-Jacobi equation, Electromagnetic field, Discrete dynamical systems and fractals, Dynamical systems, Bifurcations.

Author(s): Martin Scholtz. that of D. Schmidt to Hamiltonian systems. For other applica­ tions and related topics, we refer to the monographs of Andronov and Chaiken [1], Minorsky [1] and Thom [1].

The Hopf bifurcation refers to the development of periodic orbits ("self-oscillations") from a stable fixed point, as a parameter crosses a critical value. In Hopf's. from the very interesting (but di cult) book of Chossat-Lauterbach [2]. One other complementary reference is the book of Golubitsky-Stewart-Schae er [3].

For an elementary review on functional analysis the book of Brezis is recommanded [1]. 1Elementary bifurcation De nition In dynamical systems, a bifurcation occurs when a small smooth changeFile Size: KB. Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems.

This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. While the N-body problem could the basis of a sizable volume all by itself, the current book takes a different path.

The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. Hamiltonian Dynamical Systems: A Reprint Selection. CRC Press, ISBN: [Preview with Google Book] Problem Sets and Exams.

There are 10 problem sets. Do them all. No way you can learn the material in this course if you do not. There is.

systems. Chapter 6. Bifurcations of orbits homoclinic and heteroclinic to hyperbolic equilibria. This chapter is devoted to the generation of periodic orbits via homoclinic bifurcations. A theorem due to Andronov and Leontovich describing homoclinic bifurcation in planar continuous-time systems is.

This book has served well as a reference book and should is useful for those who are interested in going into this area. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, John Guckenheimer, Philip Holmes; This is a graduate level text and requires a fairly advanced mathematical background.

This book has three. () Limit cycle bifurcations by perturbing non-smooth Hamiltonian systems with 4 switching lines via multiple parameters.

Nonlinear Analysis: Real World Applicati () Catching-up and falling behind: Effects of learning in an R&D differential game with by: Book Section Additional Information: Updated version with a correction on p Uncontrolled Keywords: bifurcations, Hamiltonian systems, symmetry, relative equilibria, reduction, stability.

Subjects: MSCthe AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory. The purpose of these notes is to give a brief survey of bifurcation theory of Hamiltonian systems with symmetry; they are a slightly extended version of the 5 lectures given by JM on Hamiltonian Systems with Symmetry at the Peyresq Summer School.

Attention is focussed on bifurcations near equilibrium solutions and relative equilibria. [Taken from introduction]Cited by: This paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits.

By using the first-order Melnikov function of the piecewise near-Hamiltonian system, we investigate the maximal number of limit cycles that bifurcate from a global center up to first order Cited by:   Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems.

However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps.

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.

Hamiltonian Systems Web Page & Software: I will be posting a lecture schedule, homework You may use any reference book; however please do not search the web for solutions.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York, Springer-Verlag. Hale, J. and H. Koçak (). Dynamics and Bifurcations. This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum.

This includes a classification of the topological bifurcations and a dynamical characterization of. Bifurcation theory for finitely smooth planar autonomous differential systems was considered in [38].

Limit Cycles and Invariant Curves in a Class of Switching Systems with Degree Four In this paper we intend to research on this dynamic behavior in a discrete population model by using the bifurcation theory and normal form method; it is a fresh.

From the reviews: "This book deals with bifurcations of invariant tori in Hamiltonian systems, in particular in near-integrable systems. The book closes with a series of appendices, in which technical or more fundamental details are summarised .Book Edition: Ed.

This paper presents a detailed discussion of scaling techniques for Hamiltonian systems of equations. These scaling techniques are used to introduce small parameters into various systems of equations in order to simplify the proofs of the existence of periodic solutions.

The discussion proceeds through a series of increasingly more complex examples taken from celestial by:. The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems.

The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems.John David Crawford: Introduction to bifurcation theory osclllatol equation y'+y+y+y =0; (a) by defining xI =y and xz —= y, we can rewrite this evolu- tion equation as a first-order system in two dimensions, X2 X2 X) X) () Clearly if higher-order derivatives in t had appeared in Eq.

(), we could still have obtained a first-order sys- tem by simply cnlaI'g1Ilg the dimension, c.g File Size: 2MB. Systems with finite degrees of freedom and with continuous models are both considered. The book combines mathematical foundation with interesting classical and modern mechanical problems.

A number of mechanical problems illustrating how bifurcations and singularities change the behavior of systems and lead to new physical phenomena are discussed.