Abstract
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.
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Acknowledgments
MC and AR were partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020. AR also acknowledges financial support from Program INVESTIGADOR FCT (IF/00107/2015). This work has greatly benefited from AR’s visit to Nizhny Novgorod University, supported by the grant RNF 14-41-00044. The authors are grateful to the referee for the careful reading of this manuscript and the valuable comments.
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Carvalho, M., Rodrigues, A.P. Complete Set of Invariants for a Bykov Attractor. Regul. Chaot. Dyn. 23, 227–247 (2018). https://doi.org/10.1134/S1560354718030012
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DOI: https://doi.org/10.1134/S1560354718030012