Rigidity of Julia sets for Henon type maps

By T. Dinh, N. Sibony. 2013

49 citations recorded by the source corpus.

We prove that the Julia set of a Henon type automorphism on C^2 is very rigid: it supports a unique positive ddc-closed current of mass 1. A similar property holds for the cohomology class of the Green current associated with an automorphism of positive entropy on a compact Kaehler surface. Relations between this phenomenon, several quantitative equidistribution properties and the theory of value distribution will be discussed. We also survey some rigidity properties of Henon type maps on C^k and of automorphisms of compact Kaehler manifolds.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a693d5724f597be554e8114e712ee0229c78b06c

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In Condensed Matter Physics

1. Franccois Berteloot
2. Fabrizio Bianchi
3. Christophe Dupont

In Mathematical Physics

1. T. Dinh
2. N. Sibony
3. Franccois Berteloot
4. Christophe Dupont
5. Fabrizio Bianchi
6. Nguyen-Bac Dang
7. De-Qi Zhang
8. Tuyen T. T. Truong

In Statistics and Probability

1. N. Sibony
2. T. Dinh

Citations in the corpus

• Equidistribution problems of complex dynamics in higher dimension (2016, background): “Note that one can obtain similar properties for holomorphic automorphisms of a compact Kähler manifold, see [9, 35, 38] for details.”
• Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k) (2014, background): “It has been introduced by Pham [Pha] in the more general context of polynomial like mappings (see also the lecture notes by Dinh and Sibony [DS3, section 2.5]).”