TY - JOUR
T1 - Homoclinic bifurcations and uniform hyperbolicity for three-dimensions flows
AU - Arroyo, Aubin
AU - Rodriguez Hertz, Federico
N1 - Funding Information:
∗Corresponding author. E-mail addresses: [email protected] (A. Arroyo), [email protected] (F. Rodriguez Hertz). 1Partially supported by CNPq-Brazil and CONACYT-México. 2Partially supported by CNPq-Brazil.
PY - 2003
Y1 - 2003
N2 - In this paper we prove that any C1 vector field defined on a three-dimensional manifold can be approximated by one that is uniformly hyperbolic, or that exhibits either a homoclinic tangency or a singular cycle. This proves an analogous statement of a conjecture of Palis for diffeomorphisms in the context of C1-flows on three manifolds. For that, we rely on the notion of dominated splitting for the associated linear Poincaré flow.
AB - In this paper we prove that any C1 vector field defined on a three-dimensional manifold can be approximated by one that is uniformly hyperbolic, or that exhibits either a homoclinic tangency or a singular cycle. This proves an analogous statement of a conjecture of Palis for diffeomorphisms in the context of C1-flows on three manifolds. For that, we rely on the notion of dominated splitting for the associated linear Poincaré flow.
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U2 - 10.1016/S0294-1449(03)00016-7
DO - 10.1016/S0294-1449(03)00016-7
M3 - Article
AN - SCOPUS:0346724412
SN - 0294-1449
VL - 20
SP - 805
EP - 841
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 5
ER -