Browsing by Subject "Fractal Geometry"

Now showing 1 - 2 of 2
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    Accessibility of the Boundary of the Thurston Set
    (Taylor & Francis, 2023) Silvestri, Stefano; Pérez, Rodrigo A.; Mathematical Sciences, School of Science
    Consider two objects associated to the Iterated Function System (IFS) {1+𝜆⁢𝑧,−1+𝜆⁢𝑧}: the locus ℳ of parameters 𝜆∈𝔻∖{0} for which the corresponding attractor is connected; and the locus ℳ0 of parameters for which the related attractor contains 0. The set ℳ can also be characterized as the locus of parameters for which the attractor of the IFS {1+𝜆⁢𝑧,𝜆⁢𝑧,−1+𝜆⁢𝑧} contains 𝜆−1. Exploiting the asymptotic similarity of ℳ and ℳ0 with the respective associated attractors, we give sufficient conditions on 𝜆∈∂ℳ or ∂ℳ0 to guarantee it is path accessible from the complement 𝔻∖ℳ.
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    The Dynamics of Semigroups of Contraction Similarities on the Plane
    (2019-08) Silvestri, Stefano; Perez, Rodrigo; Geller, William; Misiurewicz, Michal; Roeder, Roland K.
    Given a parametrized family of Iterated Function System (IFS) we give sufficient conditions for a parameter on the boundary of the connectedness locus, M, to be accessible from the complement of M. Moreover, we provide a few examples of such parameters and describe how they are connected to Misiurewicz parameter in the Mandelbrot set, i.e. the connectedness locus of the quadratic family z^2+c.