Entropy of meromorphic maps and dynamics of birational maps

By H. Thélin, Gabriel Vigny. 2008

54 citations recorded by the source corpus.

We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then, we study the particular case of a family of generic birational maps of P^k for which we construct the Green currents and the equilibrium measure. We use for that the theory of super-potentials. We show that the measure is mixing and gives no mass to pluripolar sets. Using the criterion we get that the measure is of maximal entropy. It implies finally that the measure is hyperbolic.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df71d880282d620c7ce350d5b0dca79451a93863

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. N. Sibony
2. T. Dinh
3. Tuyen T. T. Truong
4. Nguyen-Bac Dang
5. De-Qi Zhang
6. Romain Dujardin
7. Keiji Oguiso

In Mathematical Physics

1. T. Dinh
2. N. Sibony
3. Nguyen-Bac Dang
4. De-Qi Zhang
5. Franccois Berteloot
6. Tuyen T. T. Truong
7. Romain Dujardin
8. Vincent Guedj

Citations in the corpus

• Density of positive closed currents, a theory of non-generic intersections (2012, methodology): “ersection for positive closed currents of higher bi-degree. A partial answer to this question was given by the authors in [18, 19] with applications in dynamics, see also Ahn [1] and de Th´elin-Vigny [11]. In this paper, we develop a new idea which leads to an intrinsic notion of intersection in a q”