Displaying similar documents to “Complex a priori bounds revisited”

Dynamics of quadratic polynomials : complex bounds for real maps

Mikhail Lyubich, Michael Yampolsky (1997)

Annales de l'institut Fourier

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We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map z ↦ z 2 + c , c ∈ [ - 2 , 1 / 4 ] , is locally connected.

A Proof of Simultaneous Linearization with a Polylog Estimate

Tomoki Kawahira (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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We give an alternative proof of simultaneous linearization recently shown by T. Ueda, which connects the Schröder equation and the Abel equation analytically. In fact, we generalize Ueda's original result so that we may apply it to the parabolic fixed points with multiple petals. As an application, we show a continuity result on linearizing coordinates in complex dynamics.

New a priori estimates for nondiagonal strongly nonlinear parabolic systems

Arina Arkhipova (2008)

Banach Center Publications

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We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the...

The parabolic-parabolic Keller-Segel equation

Kleber Carrapatoso (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

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I present in this note recent results on the uniqueness and stability for the parabolic-parabolic Keller-Segel equation on the plane, obtained in collaboration with S. Mischler in [11].