LAUSR

Dynamics and limiting behavior of Julia sets of König's method for multiple roots

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1 Published in 2018 at "Topology and its Applications"

DOI: 10.1016/j.topol.2017.10.013

Abstract: Abstract A well known result of J. Hubbard, D. Schleicher and S. Sutherland (see [27] ) shows that if f is a complex polynomial of degree d , then there is a finite set S… read more here.

Keywords: dynamics limiting; method multiple; multiple roots; behavior julia ... See more keywords

Conformal equivalence of measures and dynamics of orthogonal polynomials

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0 Published in 2019 at "Journal of Difference Equations and Applications"

DOI: 10.1080/10236198.2019.1648446

Abstract: ABSTRACT We introduce a notion of asymptotically orthonormal polynomials for a Borel measure μ with compact non-polar support in . Such sequences of polynomials have similar convergence properties of the sequences of Julia sets and… read more here.

Keywords: asymptotically orthonormal; dynamics orthogonal; orthonormal polynomials; convergence properties ... See more keywords

Entire functions whose Julia sets include any finitely many copies of quadratic Julia sets

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1 Published in 2017 at "Nonlinearity"

DOI: 10.1088/1361-6544/aa6c01

Abstract: We prove that for any finite collection of quadratic Julia sets, a polynomial and a transcendental entire function exist whose Julia sets include copies of the given quadratic Julia sets. In order to prove the… read more here.

Keywords: sets include; functions whose; quadratic julia; whose julia ... See more keywords

Consensus of Julia Sets of Potts Models on Diamond-Like Hierarchical Lattice

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1 Published in 2022 at "IEEE Access"

DOI: 10.1109/access.2022.3226622

Abstract: The limit sets of zeros of the partition function for $\lambda $ -state Potts models on diamond-like hierarchical lattice are the Julia sets of functions in a family of rational functions. In this paper, the… read more here.

Keywords: models diamond; consensus; julia; diamond like ... See more keywords

Julia sets of complex Hénon maps

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1 Published in 2017 at "International Journal of Mathematics"

DOI: 10.1142/s0129167x18500477

Abstract: There are two natural definitions of the Julia set for complex Henon maps: the sets J and J⋆. Whether these two sets are always equal is one of the main open questions in the field. We prove… read more here.

Keywords: complex non; julia sets; sets complex; non maps ... See more keywords