A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
Abstract In the context of nonhyperbolic chaotic scattering, it has been shown that the evolution of the KAM islands exhibits four abrupt metamorphoses that strongly affect the predictability of Hamiltonian systems. It has been suggested that these metamorphoses are related to significant changes in the structure of the KAM islands. However, previous research has not provided an explanation of the mechanisms underlying the metamorphoses. Here, we show that they occur due to the formation of a homoclinic or heteroclinic tangle that breaks the internal structure of the main KAM island. We obtain similar qualitative results in a two-dimensional Hamiltonian system and a twodimensional area-preserving map. The equivalence of the results obtained in both systems suggests that the same four metamorphoses play an important role in conservative systems.
Acknowledgements The work of A. R. N., J. M. S., and M. A. F. S. has been financially supported by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Project No. PID2019-105554GB-I00. The work of R. B. has been supported by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Projects No. PGC2018-096026-B-I00 and PID2021-122961NB-I00, and European Regional Development Fund and Diputación General de Aragón under Projects No. E24-17R and LMP124-18. Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.
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