https://doi.org/10.1140/epjs/s11734-025-01872-w
Regular Article
Convergence of orbits to the stationary state for a two-dimensional nonlinear mapping
1
Departamento de Física, UNESP – Univ Estadual Paulista, Av.24A, 1515 Bela Vista, 13506-900, Rio Claro, SP, Brazil
2
UNESP – Univ Estadual Paulista, Câmpus de São João da Boa Vista, SP, Brazil
Received:
11
April
2025
Accepted:
17
August
2025
Published online:
26
August
2025
A two-dimensional nonlinear mapping described in the action and angle variables is considered. The mapping is parameterized by a control parameter that controls the intensity of nonlinearity, by a parameter controlling the amount of dissipation, and by a dynamical exponent such that for certain choices of its values and naming the action and angle variables, we recover different mappings known in the literature. Our main research focus was to analyze the convergence of orbits to the steady state through a robust phenomenological description of the scaling approach at bifurcation, which led us to obtain a set of critical exponents that define universality classes of bifurcations. We advanced our studies using Lyapunov exponents to characterize chaos and carefully investigate the phenomenon known as boundary crises to analyze the crossing of stable and unstable manifolds.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
