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Book
ISBN: 3030991237 3030991253 Year: 2022 Publisher: Cham, Switzerland : Springer,
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Combinatorial dynamics. --- Differential equations. --- Dynamics --- Mathematics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- 517.91 Differential equations --- Differential equations --- Dynamics, Combinatorial --- Periodic orbits, Types of (Mathematics) --- Types of periodic orbits (Mathematics) --- Differentiable dynamical systems --- Dinàmica combinatòria --- Sistemes dinàmics diferenciables
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ISBN: 9781470441760 Year: 2020 Publisher: Providence, RI : American Mathematical Society,
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"The so-called "pinched disk" model of the Mandelbrot set is due to A. Douady, J. H. Hubbard and W. P. Thurston. It can be described in the language of geodesic laminations. The combinatorial model is the quotient space of the unit disk under an equivalence relation that, loosely speaking, "pinches" the disk in the plane (whence the name of the model). The significance of the model lies in particular in the fact that this quotient is planar and therefore can be easily visualized. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated MLC conjecture stating that the Mandelbrot set is locally connected. For parameter spaces of higher degree polynomials no combinatorial model is known. One possible reason may be that the higher degree analog of the MLC conjecture is known to be false. We investigate to which extent a geodesic lamination is determined by the location of its critical sets and when different choices of critical sets lead to essentially the same lamination. This yields models of various parameter spaces of laminations similar to the "pinched disk" model of the Mandelbrot set"--
Geodesics (Mathematics) --- Polynomials. --- Invariant manifolds. --- Combinatorial analysis. --- Dynamics. --- Géodésiques (mathématiques) --- Polynômes. --- Variétés invariantes. --- Analyse combinatoire. --- Dynamique.
Book
ISBN: 9780821884881 Year: 2013 Publisher: Providence American Mathematical Society
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Topology --- Fixed point theory. --- Théorème du point fixe --- 51 <082.1> --- Mathematics--Series --- Théorème du point fixe --- Fixed point theory --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics)
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