Denis Gaidashev

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Abstract. The paper concerns numerical algorithms for solving the Beltrami equation fz̄(z) = μ(z)fz(z) for a compactly supported μ. First, we study an efficient algorithm that has been proposed in the literature, and present its rigorous justification. We then propose a different scheme for solving the Beltrami equation which has a comparable speed and(More)
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R. A renormalization approach has been used in (Eckmann et al 1982) and (Eckmann et al 1984) in a computer-assisted proof of existence of a “universal” areapreserving map F∗ — a map with orbits of all binary periods 2 , k ∈ N. In(More)
We study one of the central open questions in one-dimensional renormalization theory – the conjectural universality of golden-mean Siegel disks. We present an approach to the problem based on cylinder renormalization proposed by the second author. Numerical implementation of this approach relies on the Constructive Measurable Riemann Mapping Theorem proved(More)
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R2. A renormalization approach has been used in (Eckmann et al 1982) and (Eckmann et al 1984) in a computer-assisted proof of existence of a “universal” area-preserving map F∗ — a map with orbits of all binary periods 2k, k ∈ N.(More)
The period doubling Cantor sets of strongly dissipative Hénon-like maps with different average Jacobian are not smoothly conjugated. The Jacobian Rigidity Conjecture says that the period doubling Cantor sets of two-dimensional Hénon-like maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, e.g. the(More)
It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R. A renormalization approach has been used in a computer-assisted proof of existence of an area-preserving map with orbits of all binary periods in [EKW1] and [EKW2]. As it is the case with all non-trivial universality(More)
Complex topological K-theory is defined to be the Grothendieck group of stable isomorphism classes of complex vector bundles. This construction is functorial and it is shown that the functor can be represented by homotopy classes of maps into a classifying space, for which we present an explicit model. Morse theory is then introduced and used to prove Bott(More)
We study one of the central open questions in one-dimensional renormalization theory – the conjectural universality of golden-mean Siegel disks. We present an approach to the problem based on cylinder renormalization proposed by the second author. Numerical implementation of this approach relies on the Constructive Measurable Riemann Mapping Theorem proved(More)
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