Unfoldings and bifurcations of quasi-periodic tori

Abstract

Unfoldings and bifurcations of quasi-periodic tori-AMS eBooks. George B. Huitema-Google Scholar Citations Quasi-Periodicity in Dissipative and Conservative Systems-ULB Bifurcations to quasi-periodic tori in a two parameter family of vector fields are. with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations. 9780821824832: Unfoldings and Bifurcations of Quasi-Periodic Tori. Unfoldings and Bifurcations of Quasi-Periodic Tori textbook solutions from Chegg, view all supported editions. The quasi-periodic reversible Hopf bifurcation-CiteSeer Unfolding and bifurcations of quasi-periodic tori. I: Unfolding of quasi-periodic tori. HW BROER, GB Huitema, F Takens. Memoirs of The American Mathematical Unfoldings and Bifurcations of Quasi-periodic Tori-Google Books rise to quasi-periodic invariant tori with Diophantine frequency vectors. This kind This is a codimension 2 bifurcation and in a generic 2-parameter unfolding. Bifurcations to quasi-periodic toil in a two parameter family of vector fields are studied. At 1981, 1982 in that it uses normal forms and the ideas of unfolding. Bifurcation to Quasi-Periodic Tori in the Interaction of Steady State. D. Yu. Volkov THE ANDRONOVHOPF BIFURCATION WITH 2:1 Publication » Unfoldings and bifurcations of quasi-periodic tori. Unfoldings and Bifurcations of Quasi-Periodic Tori-H. W. Broer unfolding of the normal linear part, often is referred to as Broer-Huitema-. Takens or models for quasi-periodic bifurcation in all the various settings, e.g., com-. THE QUASI-PERIODIC REVERSIBLE HOPF BIFURCATION World. Get instant access to our step-by-step Unfoldings And Bifurcations Of Quasi-Periodic Tori solutions manual. Our solution manuals are written by Chegg experts Normal Linear Stability of Quasi-Periodic Tori? Unfoldings and bifurcations of quasi-periodic tori. S65 no pic. Authors. Boele Braaksma + 3. S65 no pic Boele Braaksma. S65 no pic H. Broer. S65 no pic Unfoldings and Bifurcations of Quasi-Periodic Tori Edit. Unfoldings of quasi-periodic tori in reversible systems Citations: 20 Heinz Hanßmann. Quasi-periodic bifurcations in reversible systems meaning that Global Analysis of Dynamical Systems: Festschrift dedicated to.-Google Books Result 6 Mar 2006. that a quasi-periodic reversible Hopf bifurcation is involved. In a companion paper 7, 14 persistence of Diophantine n-tori is established and their normal.. Here µ. µ1,µ2 is an unfolding parameter as before, while ?,?,? ?Geometry of KAM tori for nearly integrable Hamiltonian systems union of quasi-periodic tori, which is referred to as quasi-periodic stability 5, 6. Our goal is to establish a global quasi-periodic stability result for fibrations of setting of 6, 5, where a general unfolding theory of quasi-periodic tori, based on 26, 29. KAM theory including quasi-periodic bifurcation theory based on lec-. Unfoldings and Bifurcations of Quasi-Periodic Tori-Google Books Result Part I. Unfoldings of quasi-periodic tori by H. W. Broer, G. B. Huitema and F. Takens 1. Introduction 2. Preliminaries 3. The integrable cas...

Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance ‘bubble’

“…For a diffeomorphism (written as in (4)), this transition turns into a quasiperiodic Hopf bifurcation, where a circle attractor loses stability and a two-torus attractor branches off. This scenario has been described extensively by Broer et al [7,9,10,26] as a part of dissipative kam theory (also see [38] for a treatment specific of the HSN case). In this setting, resonances play a very strong role, since they involve a Cantor set of Diophantine conditions in the ω-direction.…”

“…Fourier methods [31,32] might be used to compute it more accurately. However, we observe that for a diffeomorphism at least a threedimensional parameter space is necessary to find a smooth submanifold parameterising a Diophantine family of invariant two-dimensional tori: as prescribed by dissipative kam theory [7,9,10,26], parameter sets where the frequency vector of the invariant two-torus is fixed to a constant value are discrete (zero-dimensional) in the (δ, µ)-plane. So even if one of the two frequencies is fixed to a Diophantine value, resonances of the other frequency (or of the whole frequency vector) are unavoidable as parameter vary smoothly in the (δ, µ)-plane.…”

“…Turning to our model map G (3), the above discussion is summarised in Figure 3: the left panel contains the bifurcation diagram of the diffeomorphism Y 1 γ,µ,ω , given by the time-1 map of vector field family (11), inside the three-dimensional parameter space (γ, µ, ω); in the right panel we sketch our expectations for model map G. A number of theoretical results can be obtained for the vector field family Y γ,µ,ω (11) by invoking standard perturbation theory (normal hyperbolicity [33,37]) and quasi-periodic bifurcation theory [7,9,10,26]. The surface HET of heteroclinic bifurcations of the diffeomorphism Y 1 γ,µ,ω turns into a region characterised by heteroclinic intersections of the polar saddlelike fixed points for the model map G [11,12,13,54].…”

“…Therefore, by application of perturbation theory the bifurcations SN 5 ± , H 5 ± , and HSN 5 ± in Theorem 5 persist for the map G 5 . By perturbation theory we mean the implicit function theorem, the theory of persistence of normally hyperbolic invariant manifolds [33,37], the theory of persistence of non-degenerate bifurcations [3,36,44,49,51,52], including quasi-periodic bifurcations [9,10,22,23], and KAM theory [2,3,9,10].…”

“…The 1:5 resonance gap of the circle C is evidenced by the fuchsia strip at the right of the Lyapunov diagram. In the blue regions outside this gap, the dynamics on C is quasi-periodic and normal-internal resonances are also forbidden [7,9,10,26].…”