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Alexandre Rodrigues

University of Porto


Carvalho M., Rodrigues A. P.
Complete Set of Invariants for a Bykov Attractor
2018, vol. 23, no. 3, pp.  227-247
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 behavior and, from the asymptotic properties of these nonconverging 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.
Keywords: Bykov attractor, historic behavior, conjugacy, complete set of invariants
Citation: Carvalho M., Rodrigues A. P.,  Complete Set of Invariants for a Bykov Attractor, Regular and Chaotic Dynamics, 2018, vol. 23, no. 3, pp. 227-247

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