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math.DS2012
On the scaling ratios for Siegel disks
Denis Gaidashev
The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point and the rotation number whose continued fraction expansion is preperiodic has…
math.DS2012★ 9 cited
Rigidity for infinitely renormalizable area-preserving maps
Denis Gaidashev, Tomas Johnson, Marco Martens
The period doubling Cantor sets of strongly dissipative Henon-like maps with different average Jacobian are not smoothly conjugated. The Jacobian Rigidity Conjecture says that the…
math.DS2012
Renormalization for Lorenz maps of monotone combinatorial types
Denis Gaidashev
Lorenz maps are maps of the unit interval with one critical point of order rho>1, and a discontinuity at that point. They appear as return maps of leafs of sections of the geometri…