On non-smooth pitchfork bifurcations in invertible quasi-periodically forced 1-D maps

Jorba Monte, ÀngelTatjer Montaña, Joan CarlesMuñoz Almaraz, Francisco JavierProducción Científica UCH 2018UCH. Departamento de Matemáticas, Física y Ciencias Tecnológicas2019-11-202019-11-202018-11-20Jorba, À., Muñoz-Almaraz, FJ. & Tatjer, JC. (2018). On non-smooth pitchfork bifurcations in invertible quasi-periodically forced 1-D maps. Journal of Difference Equations and Applications, vol. 24, n. 4, pp. 588-608. DOI: https://doi.org/10.1080/10236198.2017.13318891023-61981563-5120 (Electrónico)http://hdl.handle.net/10637/10710Este artículo se encuentra disponible en la página web de la revista en la siguiente URL: https://www.tandfonline.com/doi/abs/10.1080/10236198.2017.1331889This is the pre-peer reviewed version of the following article: Jorba, À., Muñoz-Almaraz, FJ. & Tatjer, JC. (2018). On non-smooth pitchfork bifurcations in invertible quasi-periodically forced 1-D maps. Journal of Difference Equations and Applications, vol. 24, n. 4, pp. 588-608, which has been published in final form at https://doi.org/10.1080/10236198.2017.1331889Este es el pre-print del siguiente artículo: Jorba, À., Muñoz-Almaraz, FJ. & Tatjer, JC. (2018). On non-smooth pitchfork bifurcations in invertible quasi-periodically forced 1-D maps. Journal of Difference Equations and Applications, vol. 24, n. 4, pp. 588-608, que se ha publicado de forma definitiva en https://doi.org/10.1080/10236198.2017.1331889In this note we revisit an example introduced by T. J ager in which a Strange Nonchaotic Attractor seems to appear during a pitchfork bifurcation of invariant curves in a quasi-periodically forced 1-d map. In this example, it is remarkable that the map is invertible and, hence, the invariant curves are always reducible. In the rst part of the paper we give a numerical description (based on a precise computation of invariant curves and Lyapunov exponents) of the phenomenon. The second part consists in a preliminary study of the phenomenon, in which we prove that an analytic self-symmetric invariant curve is persistent under perturbations.application/pdfesopen accessSistemas dinámicos diferenciables.Differentiable dynamical systems.Curvas.Symmetry.Differential equations.Curves.Simetría.Ecuaciones diferenciales.On non-smooth pitchfork bifurcations in invertible quasi-periodically forced 1-D mapsArtículohttps://doi.org/10.1080/10236198.2017.1331889https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es