@incollection{AST_2003__286__223_0,
author = {Broer, Henk},
title = {Coupled {Hopf-bifurcations:} {Persistent} examples of $n$-quasiperiodicity determined by families of 3-jets},
booktitle = {Geometric methods in dynamics (I) : Volume in honor of Jacob Palis},
editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe},
series = {Ast\'erisque},
pages = {223--229},
publisher = {Soci\'et\'e math\'ematique de France},
number = {286},
year = {2003},
mrnumber = {2052303},
zbl = {1039.37030},
language = {en},
url = {http://www.numdam.org/item/AST_2003__286__223_0/}
}
TY - CHAP AU - Broer, Henk TI - Coupled Hopf-bifurcations: Persistent examples of $n$-quasiperiodicity determined by families of 3-jets BT - Geometric methods in dynamics (I) : Volume in honor of Jacob Palis AU - Collectif ED - de Melo, Wellington ED - Viana, Marcelo ED - Yoccoz, Jean-Christophe T3 - Astérisque PY - 2003 SP - 223 EP - 229 IS - 286 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2003__286__223_0/ LA - en ID - AST_2003__286__223_0 ER -
%0 Book Section %A Broer, Henk %T Coupled Hopf-bifurcations: Persistent examples of $n$-quasiperiodicity determined by families of 3-jets %B Geometric methods in dynamics (I) : Volume in honor of Jacob Palis %A Collectif %E de Melo, Wellington %E Viana, Marcelo %E Yoccoz, Jean-Christophe %S Astérisque %D 2003 %P 223-229 %N 286 %I Société mathématique de France %U http://www.numdam.org/item/AST_2003__286__223_0/ %G en %F AST_2003__286__223_0
Broer, Henk. Coupled Hopf-bifurcations: Persistent examples of $n$-quasiperiodicity determined by families of 3-jets, dans Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 223-229. http://www.numdam.org/item/AST_2003__286__223_0/
[1] , , and , Three coupled oscillators: Mode-locking, global bifurcation and toroidal chaos, Physica D, (1991), 387-475. | DOI | MR | Zbl
[2] & , On a quasi-periodic Hopf bifurcation, Ann. Institut Henri Poincaré, Analyse non linéaire, 4, no.2 (1987), 115-168. | DOI | EuDML | Numdam | MR | Zbl
[3] , and , Towards a Quasiperiodic Bifurcation Theory, Mem. AMS, 83(421) (1990), 83-175. | Zbl
[4] , Formal normal forms for vector fields and some consequences for bifurcations in the volume preserving case. In: D. Rand and L.S. Young (eds.), Dynamical Systems and Turbulence, Warwick 1980 LNM 898 (1981), 75-89, Springer-Verlag. | MR | Zbl
[5] , KAM-Theory: Multi-Periodicity in conservative and dissipative systems, Nieuw Arch. Wish. 14(1), (1996), 1-15. | MR | Zbl
[6] , and , Unfoldings of Quasi-Periodic Tori, Mem. AMS, 83(421) (1990), 1-82. | Zbl
[7] , and , Quasi-periodic tori in families of dynamical systems: order amidst chaos, LNM 1645, Springer Verlag 1996. | Zbl
[8] & , Mixed spectrum and rotational symmetry, Arch. Rational Mech. An. 124 (1993), 13-42. | DOI | MR | Zbl
[9] , and , Integrable and non-integrable deformations of the skew Hopf bifurcation, Reg. and Chaot. Dyn. 4 (1999), 17-43. | DOI | MR | Zbl
[10] and , Quasi-periodic stability of subfamilies of an unfolded skew-Hopf bifurcation, Arch. Rational Mech. An. 152 (2000), 283-326. | DOI | MR | Zbl
[11] , and , Normal Forms and Bifurcation of Planar Vector Fields. Cambridge University Press 1994. | MR | Zbl
[12] and , Complicated dynamics of scalar reaction diffusion equations with a nonlocal term, Proc. Roy. Soc. Edinburgh Sect. A, (Mathematical and Physical Sciences) 115(1-2) (1990), 167-192. | DOI | MR | Zbl
[13] and , Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Appl. Math. Sciences 42, Springer Verlag 1983. | DOI | MR | Zbl
[14] , and , Invariant Manifolds, LNM 583, Springer Verlag 1977. | MR | Zbl
[15] , A mathematical example displaying features of turbulence. Commun. Appl. Math. 1 (1948), 303-322. | DOI | MR | Zbl
[16] and , On the Normal Behaviour of Partially Elliptic Lower-Dimensional Tori of Hamiltonian Systems, Nonlinearity 10 (1997), 783-822. | DOI | MR | Zbl
[17] , Convergent series expansions for quasi-periodic motions, Math. Ann. 169 (1967), 136-176. | DOI | EuDML | MR | Zbl
[18] , and , Occurrence of strange Axiom attractors near quasiperiodic flows on , Commun. Math. Phys. 64 (1978), 35-40. | DOI | MR | Zbl
[19] and , Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation, Proc. Roy. Soc. Edinburgh Sect. A, (Mathematical and Physical Sciences) 126(4) (1996), 867-884. | DOI | MR | Zbl
[20] and , On the nature of turbulence, Commun. Math. Phys. 20 (1971), 167-192; | DOI | MR | Zbl
and , On the nature of turbulence, Commun. Math. Phys. 23 (1971), 343-4. | DOI | Numdam | MR | Zbl
[21] , Perturbations of translations in the two-dimensional torus: the case near resonance, Proceedings VI CEDYA, Universidad de Zaragoza, 1984.
[22] , Singularities of Vector Fields, Commun. Math. Phys. 20, 1970, 167-192, | Zbl
, Singularities of Vector Fields, Commun. Math. Phys. 23, (1971), 343-344. | Zbl
, Singularities of Vector Fields, Publ. I.H.E.S. 43 (1974), 47-100. | DOI | EuDML | Numdam | MR | Zbl
[23] and , Resonances in skew and reducible quasi-periodic Hopf bifurcations, Nonlinearity 13 (2000), 377-396. | DOI | MR | Zbl
[24] , Centre Manifolds, Normal Forms and Elementary Bifurcations, Dynamics Reported 2 (1989), 89-170. | DOI | MR | Zbl
[25] , On the skew Hopf bifurcation. PhD thesis, University of Groningen, 1998. | Zbl
[26] , Bifurcation of a certain family of planar vector fields tangent to axes, Journ. Diff. Eqns. 67 (1987), 1-55. | DOI | MR | Zbl
