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Search Results: 1 - 10 of 44890 matches for " Michael Yampolsky "
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Siegel disks and renormalization fixed points
Michael Yampolsky
Mathematics , 2006,
Abstract: In this note we construct hyperbolic fixed points for cylinder renormalization of maps with Siegel disks.
The Attractor of Renormalization and Rigidity of Towers of Critical Circle Maps
Michael Yampolsky
Mathematics , 1998,
Abstract: We demonstrate the existence of a global attractor A with a Cantor set structure for the renormalization of critical circle mappings. The set A is invariant under a generalized renormalization transformation, whose action on A is conjugate to the two-sided shift.
Complex bounds for critical circle maps
Michael Yampolsky
Mathematics , 1995,
Abstract: We use the methods developed with M. Lyubich for proving complex bounds for real quadratics to extend E. De Faria's complex a priori bounds to all critical circle maps with an irrational rotation number. The contracting property for renormalizations of critical circle maps follows. In the Appendix we give an application of the complex bounds for proving local connectivity of some Julia sets.
Cylinder renormalization of Siegel disks
Denis Gaidashev,Michael Yampolsky
Mathematics , 2006,
Abstract: 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 by the first author. Our numerical study yields a convincing evidence to support the Hyperbolicity Conjecture in this setting.
On computability of Julia sets: answers to questions of Milnor and Shub
Mark Braverman,Michael Yampolsky
Mathematics , 2006,
Abstract: In this note we give answers to questions posed to us by J.Milnor and M.Shub, which shed further light on the structure of non-computable Julia sets.
Geometrization of postcritically finite branched coverings
Sylvain Bonnot,Michael Yampolsky
Mathematics , 2010,
Abstract: We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K.~Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurston obstruction. It is thus Thurston equivalent to a rational map.
Hyperbolicity of renormalization of circle maps with a break-type singularity
Konstantin Khanin,Michael Yampolsky
Mathematics , 2013,
Abstract: We study the renormalization operator of circle homeomorphisms with a break point and show that it possesses a hyperbolic horseshoe attractor.
Poly-time Computability of the Feigenbaum Julia set
Artem Dudko,Michael Yampolsky
Mathematics , 2014, DOI: 10.1017/etds.2015.24
Abstract: We present the first example of a poly-time computable Julia set with a recurrent critical point: we prove that the Julia set of the Feigenbaum map is computable in polynomial time.
Dynamics of quadratic polynomials: Complex bounds for real maps
Mikhail Lyubich,Michael Yampolsky
Mathematics , 1995,
Abstract: We extend Sullivan's complex a priori bounds to real quadratic polynomials with essentially bounded combinatorics. Combined with the previous results of the first author, this yields complex bounds for all real quadratics. Local connectivity of the corresponding Julia sets follows.
Mating non-renormalizable quadratic polynomials
Magnus Aspenberg,Michael Yampolsky
Mathematics , 2006,
Abstract: In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and does not have any non-repelling periodic orbits.
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