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A Proof of Simultaneous Linearization with a Polylog Estimate

100%

Kawahira T.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom 55

nr 1

43-52

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.

Topology of the regular part for infinitely renormalizable quadratic polynomials

63%

Cabrera C., Kawahira T.

Fundamenta Mathematicae

2010

tom 208

nr 1

35-56

We describe the well studied process of renormalization of quadratic polynomials from the point of view of their natural extensions. In particular, we describe the topology of the inverse limit of infinitely renormalizable quadratic polynomials and prove that when they satisfy a priori bounds, the topology is rigid modulo combinatorial equivalence.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Fundamenta Mathematicae

2 Kawahira T.

1 Cabrera C.

1 2010

1 2007

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A Proof of Simultaneous Linearization with a Polylog Estimate

Topology of the regular part for infinitely renormalizable quadratic polynomials