Periodic Solutions of Nonlinear Dynamical Systems, Eduard Reithmeier
Автор: Leonid Pastur; Alexander Figotin Название: Spectra of Random and Almost-Periodic Operators ISBN: 364274348X ISBN-13(EAN): 9783642743481 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is so not only because of the subject`s position at the in- tersection of operator spectral theory, probability theory and mathematical physics, but also because of its importance to theoretical physics, and par- ticularly to the theory of disordered condensed systems.
Автор: A.I. Stepanets Название: Classification and Approximation of Periodic Functions ISBN: 0792336038 ISBN-13(EAN): 9780792336037 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The chapters are split into sections, which, in turn, are split into subsections enumerated by two numbers: the first stands for the number of the section while the second for the number ofthe subsection itself. The same numeration is used for all kinds of statements and formulas. If we refer to statements or formulas in other chapters, we use triple numeration where the first number stands for the chapter and the other two have the same sense. The results presented in this book were discussed on the seminars at the Institute of Mathematics of Ukrainian Academy ofSciences, at the Steklov Mathematical Institute of the Academy of Sciences of the USSR, at Moscow and Tbilisi State Universities. I am deeply grateful to the heads of these seminars Professors V. K. Dzyadyk, N. P. Kor- neichuk, S. B. Stechkin, P. L. U1yanov, and L. V. Zhizhiashvili as well as to the mem- bers ofthese seminars that took an active part in the discussions. In TRODUCTIon It is well known for many years that every 21t -periodic summable function f(x) can be associated in a one-to-one manner with its Fourier series (1. 1) Slfl where I It = - f f(t)cosktdt 1t -It and I It - f f(t)sinktdt. 1t -It Therefore, if for approximation of a given function f(-), it is necessary to construct a sequence ofpolynomials Pn (.
Автор: A. Ambrosetti; V. Coti-Zelati Название: Periodic Solutions of Singular Lagrangian Systems ISBN: 0817636552 ISBN-13(EAN): 9780817636555 Издательство: Springer Рейтинг: Цена: 14673.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Hendrik W. Broer; George B. Huitema; Mikhail B. Se Название: Quasi-Periodic Motions in Families of Dynamical Systems ISBN: 3540620257 ISBN-13(EAN): 9783540620259 Издательство: Springer Рейтинг: Цена: 6282.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. 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.
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 Рейтинг: Цена: 28929.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Proceedings of the NATO Advanced Research Workshop, Il Ciocco, Italy, October 13-17, 1986
Автор: A. Ambrosetti; V. Coti-Zelati Название: Periodic Solutions of Singular Lagrangian Systems ISBN: 1461267056 ISBN-13(EAN): 9781461267058 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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)
Описание: Chapter 1. Introduction.- Chapter 2. Positive Periodic Solutions of Nonlinear Functional Differential Equations with Parameter λ.- Chapter 3. Multiple Periodic Solutions of a System of Functional Differential Equations.- Chapter 4. Multiple Periodic Solutions of Nonlinear Functional Differential Equations.- Chapter 5. Asymptotic Behavior of Periodic Solutions of Differential Equations of First Order.- Bibliography.
Автор: Bernold Fiedler Название: Global Bifurcation of Periodic Solutions with Symmetry ISBN: 3540192344 ISBN-13(EAN): 9783540192343 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? This book probes these questions.
Автор: Otto Vejvoda; L. Herrmann; V. Lovicar; M. Sova; I. Название: Partial differential equations: time-periodic solutions ISBN: 9024727723 ISBN-13(EAN): 9789024727728 Издательство: Springer Рейтинг: Цена: 34799.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Luo Название: Periodic Flows to Chaos in Time-delay Systems ISBN: 331942663X ISBN-13(EAN): 9783319426631 Издательство: Springer Рейтинг: Цена: 16070.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems.
Автор: Llibre, Jaume Moeckel, Richard Simo, Carles Название: Central configurations, periodic orbits, and hamiltonian systems ISBN: 3034809328 ISBN-13(EAN): 9783034809320 Издательство: Springer Рейтинг: Цена: 4191.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
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