Quasi-Periodic Motions in Families of Dynamical Systems, Hendrik W. Broer; George B. Huitema; Mikhail B. Se

Автор: A. Ambrosetti; V. Coti-Zelati
Название: Periodic Solutions of Singular Lagrangian Systems
ISBN: 1461267056 ISBN-13(EAN): 9781461267058
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Описание: Thismonographdealswiththeexistenceofperiodicmotionsof Lagrangiansystemswith ndegreesoffreedom ij + V'(q) =0, where Visasingularpotential.Aprototypeofsuchaproblem, evenifitisnottheonlyphysicallyinterestingone, istheKepler problem .. q 0 q+yqr= . This, jointlywiththemoregeneralN-bodyproblem, hasalways beentheobjectofagreatdealofresearch.Mostofthoseresults arebasedonperturbationmethods, andmakeuseofthespecific featuresoftheKeplerpotential. OurapproachismoreonthelinesofNonlinearFunctional Analysis: ourmainpurposeistogiveafunctionalframefor systemswithsingularpotentials, includingtheKeplerandthe N-bodyproblemasparticularcases.PreciselyweuseCritical PointTheorytoobtainexistenceresults, qualitativeinnature, whichholdtrueforbroadclassesofpotentials.Thishighlights thatthevariationalmethods, whichhavebeenemployedtoob- tainimportantadvancesinthestudyofregularHamiltonian systems, canbesuccessfallyusedtohandlesingularpotentials aswell. Theresearchonthistopicisstillinevolution, andtherefore theresultswewillpresentarenottobeintendedasthefinal ones. Indeedamajorpurposeofourdiscussionistopresent methodsandtoolswhichhavebeenusedinstudyingsuchprob- lems. Vlll PREFACE Partofthematerialofthisvolumehasbeenpresentedina seriesoflecturesgivenbytheauthorsatSISSA, Trieste, whom wewouldliketothankfortheirhospitalityandsupport. We wishalsotothankUgoBessi, PaoloCaldiroli, FabioGiannoni, LouisJeanjean, LorenzoPisani, EnricoSerra, KazunakaTanaka, EnzoVitillaroforhelpfulsuggestions. May26,1993 Notation n 1.For x, yE IR, x. ydenotestheEuclideanScalarproduct, and IxltheEuclideannorm. 2. meas(A)denotestheLebesguemeasureofthesubset Aof n IR - 3.Wedenoteby ST = 0, T]/{a, T}theunitarycirclepara- metrizedby t E 0, T].Wewillalsowrite SI= ST=I. n 1 n 4.Wewillwrite sn = {xE IR +: Ixl =I}andn = IR \{O}. n 5.Wedenoteby LP( O, T], IR ),1 p +00, theLebesgue spaces, equippedwiththestandardnorm lIulip. l n l n 6. H (ST, IR )denotestheSobolevspaceof u E H,2(0, T; IR ) suchthat u(O) = u(T).Thenormin HIwillbedenoted by lIull2 = lIull + lIull - 7.Wedenoteby(-1-)and11-11respectivelythescalarproduct andthenormoftheHilbertspace E. 8.For uE E, EHilbertorBanachspace, wedenotetheball ofcenter uandradiusrby B(u, r) = {vE E: lIu- vii r}.Wewillalsowrite B = B(O, r). r 1 1 9.WesetA (n) = {uE H (St, n)}. k 10.For VE C (1Rxil, IR)wedenoteby V'(t, x)thegradient of Vwithrespectto x. l 11.Given f E C (M, IR), MHilbertmanifold, welet r = {uEM: f(u) a}, f-l(a, b) = {uE E: a f(u) b}. x NOTATION 12.Given f E C1(M, JR), MHilbertmanifold, wewilldenote by Zthesetofcriticalpointsof fon Mandby Zctheset Z U f-l(c, c). 13.Givenasequence UnE E, EHilbertspace, by Un ---"" Uwe willmeanthatthesequence Unconvergesweaklyto u. 14.With (E)wewilldenotethesetoflinearandcontinuous operatorson E. 15.With Ck''''(A, JR)wewilldenotethesetoffunctions ffrom AtoJR, ktimesdifferentiablewhosek-derivativeisHolder continuousofexponent0: . Main Assumptions Wecollecthere, forthereader'sconvenience, themainassump- tionsonthepotential Vusedthroughoutthebook. (VO) VEC1(lRXO, lR), V(t+T, x)=V(t, X) V(t, x)ElRXO, (VI) V(t, x)

Автор: Luo
Название: Analytical Periodic Flows and Chaos in Nonlinear Systems
ISBN: 1118658612 ISBN-13(EAN): 9781118658611
Издательство: Wiley
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Описание: Presents an approach to analytically determine periodic flows to chaos or quasi-periodic flows in nonlinear dynamical systems with/without time-delay. This title covers the mathematical theory and includes two examples of nonlinear systems with/without time-delay in engineering and physics.

Автор: Miklos Farkas
Название: Periodic Motions
ISBN: 1441928383 ISBN-13(EAN): 9781441928382
Издательство: Springer
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Описание: "The task is done; the Maker rests. And lo The engine turns. A million years shall flow, Ere round its axle shall the wheel run slow And a new cog be needed .... " Mad8.ch: The Tragedy of Man J.C.W. Horne's translation In this book I tried to sum up the facts and results I considered most important concerning periodic solutions of ordinary differential equations (ODEs) produced by this century from Henri Poincare up to the youngest mathematician appearing in the list of references. I have included also some results of my own that did not find their way into monographs in the past. I have done research in this direction for more than 25 years and have given graduate courses about some of the topics covered for many years at the Budapest University of Technology and also at the Universidad Central de Venezuela in Caracas. I hope that people interested in differential equations and applications may use this experience. Some may say that periodic solutions of ODEs has been a closed chapter of mathematics for some time.

Автор: Han-lin Chen
Название: Complex Harmonic Splines, Periodic Quasi-Wavelets
ISBN: 9401058431 ISBN-13(EAN): 9789401058438
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Описание: This book, written by our distinguished colleague and friend, Professor Han-Lin Chen of the Institute of Mathematics, Academia Sinica, Beijing, presents, for the first time in book form, his extensive work on complex harmonic splines with applications to wavelet analysis and the numerical solution of boundary integral equations.

Автор: Han-lin Chen
Название: Complex Harmonic Splines, Periodic Quasi-Wavelets
ISBN: 0792361377 ISBN-13(EAN): 9780792361374
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Описание: This book, written by our distinguished colleague and friend, Professor Han-Lin Chen of the Institute of Mathematics, Academia Sinica, Beijing, presents, for the first time in book form, his extensive work on complex harmonic splines with applications to wavelet analysis and the numerical solution of boundary integral equations.

Автор: Eduard Reithmeier
Название: Periodic Solutions of Nonlinear Dynamical Systems
ISBN: 3540545123 ISBN-13(EAN): 9783540545125
Издательство: Springer
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Описание: Addressing mathematicians and engineers working with nonlinear dynamics, this monograph describes the multiple shooting method, which is employed in numerically computing limit cycles. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations.

Автор: Wanda Szemplinska-Stupnicka; Gerard Iooss; Francis
Название: Chaotic Motions in Nonlinear Dynamical Systems
ISBN: 3211820620 ISBN-13(EAN): 9783211820629
Издательство: Springer
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Описание: Discoveries of chaotic, unpredictable behaviour in physical deterministic systems has brought about new analytic and experimental techniques in dynamics. This book presents both viewpoints: that of the analyst and of the experimenter.

Автор: Sergio Bittanti; Patrizio Colaneri
Название: Periodic Systems
ISBN: 1849968055 ISBN-13(EAN): 9781849968058
Издательство: Springer
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Описание: This book offers a comprehensive treatment of the theory of periodic systems, including the problems of filtering and control. It covers an array of topics, presenting an overview of the field and focusing on discrete-time signals and systems.

Автор: P.H. Rabinowitz; A. Ambrosetti; I. Ekeland; E.J. Z
Название: Periodic Solutions of Hamiltonian Systems and Related Topics
ISBN: 9027725535 ISBN-13(EAN): 9789027725530
Издательство: Springer
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Описание: Proceedings of the NATO Advanced Research Workshop, Il Ciocco, Italy, October 13-17, 1986

Автор: Llibre, Jaume Moeckel, Richard Simo, Carles
Название: Central configurations, periodic orbits, and hamiltonian systems
ISBN: 3034809328 ISBN-13(EAN): 9783034809320
Издательство: Springer
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Описание: 1 The Averaging Theory for Computing Periodic Orbits.- Introduction: the classical theory.- Averaging theory for arbitrary order and dimension.- Three applications of Theorem.- 2 Lectures on Central Configurations.- The n-body problem.- Symmetries and integrals.- Central configurations and self-similar solutions.- Matrix equations of motion.- Homographic motions of central configurations in Rd.- Albouy-Chenciner reduction and relative equilibria in Rd.- Homographic motions in Rd.- Central configurations as critical points.- Collinear central configurations.- Morse indices of non-collinear central configurations.- Morse theory for CC's and SBC's.- Dziobek configurations.- Convex Dziobek central configurations.- Generic finiteness for Dziobek central configurations.- Some open problems.- 3 Dynamical Properties of Hamiltonian Systems.- Introduction.- Low dimension.- Some theoretical results, their implementation and practical tools.- Applications to Celestial Mechanics.

Автор: A. Ambrosetti; V. Coti-Zelati
Название: Periodic Solutions of Singular Lagrangian Systems
ISBN: 0817636552 ISBN-13(EAN): 9780817636555
Издательство: Springer
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Описание: A summary and synthesis of recent research demonstrating that variational methods can be used to successfully handle systems with singular potential, the Lagrangian systems. The classic cases of the Kepler problem and the N-body problem are used as specific examples.

Автор: Valentin Afraimovich; Jos? Ant?nio Tenreiro Machad
Название: Complex Motions and Chaos in Nonlinear Systems
ISBN: 3319287621 ISBN-13(EAN): 9783319287621
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Описание: Detection of the Quasi-Periodic Processes in Experimental Measurements: Reduction to an Ideal Experiment.- Functional Differential Equations with Piecewise Constant Argument.- Singular Phenomena in Aerodynamics and the Bifurcation Analysis.- Plasma Flow Control: Progress and Problems.- Steady State Solution for a Rayleigh's Piston in a Temperature Gradient.- An Inspiration to Craft Networks Which Can Achieve Chaotic States.- Finite Element Simulations of the Nonlinear Fluid-Membrane Interactions Using a Modified Characteristic-Based Split (CBS) Scheme.- Modelling and Predicting Chaos in Local Area Network Traffic.- Centrifugal Compressor Blade Crack Classification by Using Squared Envelope and Experimental Verification.- Numerical Methods on Model Reduction and Lagrangian Coherent Structure in Fluid Dynamics.- Numerical Method for Analysis of Nonlinear Fluid-structure Coupling Effects on the Aerodynamic Performance of Airfoil at Low Reynolds Number.- On periodic motions in a time-delayed, quadratic nonlinear oscillator with periodic excitation.