Geometry of currents, intersection theory and dynamics of horizontal-like maps

By T. Dinh, N. Sibony. 2004

56 citations recorded by the source corpus.

We introduce a geometry on the cone of positive closed currents of bidegree (p, p) and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like mappings. The Green currents satisfy some extremality properties. The equilibrium measure is invariant, mixing and has maximal entropy. It is equal to the intersection of the Green currents associated to the horizontal-like map and to its inverse.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/337025923fb9a42ab8f69681e29234bb769bda1d

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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 Geometry and Topology

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

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

• Super-potentials of positive closed currents, intersection theory and dynamics (2007, background): “h, we develop the theory of intersection for positive closed currents of arbitrary bidegree. The method might be extended to currents on compact K¨ahler manifolds or in some local situation, see also [21]. Here, for simplicity, we will only consider currents in the projective space. 38 4.1 Some univ”
• Rigidity of Julia sets for Henon type maps (2013, unknown): “We refer to [10, 11, 16, 18, 19, 23, 28, 32, 33] for these developments.”