Browsing by Author "Domínguez Calderón, Igsyl"

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    Fibred non-hyperbolic quadratic families
    (2024) Domínguez Calderón, Igsyl; Ponce Acevedo, Mario; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
    The aim of this thesis is two-folding. In the initial instance, we have made signifIcant progress in the problem of density of hyperbolic components within the context of fibred quadratic polynomial dynamics by demonstrating the existence of robust non- hyperbolic fibred quadratic polynomials. Secondly, we present a more complex class of invariant sets that are distinct from the invariant curves for fibred polynomial dynamics, called multi-curves. Furthermore, a construction for multi-curves in quadratic polynomial dynamics is shown, resulting in the attainment of not only invariant multi-curves, but also with the characteristic of being attracting.