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2023-01-10

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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/195109

Breakdown of Heteroclinic Connections in the Analytic Hopf-Zero Singularity: Rigorous Computation of the Stokes Constant

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https://doi.org/10.1007/s00332-022-09882-x

Resum

Consider analytic generic unfoldings of the three- dimensional conservative Hopf-zero singularity. Under open conditions on the parameters determining the singularity, the unfolding possesses two saddle-foci when the unfolding parameter is small enough. One of them has one-dimensional stable manifold and two-dimensional unstable manifold, whereas the other one has one- dimensional unstable manifold and two-dimensional stable manifold. Baldomá et al. (J Dyn Differ Equ 25(2):335-392, 2013) gave an asymptotic formula for the distance between the one-dimensional invariant manifolds in a suitable transverse section. This distance is exponentially small with respect to the perturbative parameter, and it depends on what is usually called a Stokes constant. The nonvanishing of this constant implies that the distance between the invariant manifolds at the section is not zero. However, up to now there do not exist analytic techniques to check that condition. In this paper we provide a method for obtaining accurate rigorous computer-assisted bounds for the Stokes constant. We apply it to two concrete unfoldings of the Hopf-zero singularity, obtaining a computer-assisted proof that the constant is nonzero.

Matèries

Teoria de la bifurcació, Equacions diferencials ordinàries, Sistemes dinàmics diferenciables, Anàlisi d'error (Matemàtica)

Matèries (anglès)

Bifurcation theory, Ordinary differential equations, Differentiable dynamical systems, Error analysis (Mathematics)

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Articles publicats en revistes (Matemàtiques i Informàtica)

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BALDOMÁ BARRACA, Inmaculada, CAPIŃSKI, Maciej j., GUÀRDIA MUNÁRRIZ, Marcel, MARTÍNEZ-SEARA ALONSO, M. teresa. Breakdown of Heteroclinic Connections in the Analytic Hopf-Zero Singularity: Rigorous Computation of the Stokes Constant. _Journal of Nonlinear Science_. 2023. Vol. 33. [consulta: 20 de gener de 2026]. ISSN: 0938-8974. [Disponible a: https://hdl.handle.net/2445/195109]

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