On moduli of conjugation for some n-dimensional vector fields

Susín, Antoni; Simó, Carles

doi:10.1016/0022-0396(89)90118-6

Cited by 2 publications

(2 citation statements)

References 4 publications

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“…Bonatti and Dufraine [4] go on to extend this result to obtain a complete characterization of such a heteroclinic connection up to topological equivalence. Higher dimensional heteroclinic connections between equilibria are analyzed in a similar way by Susín and Simó [18].…”

Section: Introductionmentioning

confidence: 99%

“…Carvalho and Rodrigues [5] consider a Bykov attractor -a heteroclinic cycle between two hyperbolic equilibria on a three-dimensional sphere with a one-dimensional connection as in [7] and a two-dimensional connection as in [18] between them. Extending the argument of [20], they find a complete set of four invariants for this situation, namely a combination of the angular speeds of the equilibria, the rates of expansion and contraction in linearizing neighborhoods of them, besides information regarding the transition maps between these neighborhoods.…”

Section: Introductionmentioning

confidence: 99%

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Moduli of stability for heteroclinic cycles of periodic solutions

Carvalho¹,

Lohse²,

Rodrigues³

2019

Discrete &Amp; Continuous Dynamical Systems - A

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We consider C 2 vector fields in the three dimensional sphere with an attracting heteroclinic cycle between two periodic hyperbolic solutions with real Floquet multipliers. The proper basin of this attracting set exhibits historic behavior and from the asymptotic properties of its orbits we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. As expected, this set contains the periods of the orbits involved in the cycle, a combination of their angular speeds, the rates of expansion and contraction in linearizing neighborhoods of them, besides information regarding the transition maps and the transition times between these neighborhoods. We conclude with an application of this result to a class of cycles obtained by the lifting of an example of R. Bowen.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Moduli of stability for heteroclinic cycles of periodic solutions

Carvalho¹,

Lohse²,

Rodrigues³

2019

Discrete &Amp; Continuous Dynamical Systems - A

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Complete Set of Invariants for a Bykov Attractor

Carvalho

Rodrigues

2018

Regul. Chaot. Dyn.

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In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behaviour and, from the asymptotic properties of these non-converging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices.

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On moduli of conjugation for some n-dimensional vector fields

Cited by 2 publications

References 4 publications

Moduli of stability for heteroclinic cycles of periodic solutions

Moduli of stability for heteroclinic cycles of periodic solutions

Complete Set of Invariants for a Bykov Attractor

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