Dynamics of regular birational maps in P^k

By T. Dinh, N. Sibony. 2004

52 citations recorded by the source corpus.

Abstract We develop the study of some spaces of currents of bidegree ( p , p ) . As an application we construct the equilibrium measure for a large class of birational maps of P k , as intersection of Green currents. We show that these currents are extremal and that the corresponding measure is mixing.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dfe6d97015febbbb64b5066034543a9f1be0a01f

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Geometry of currents, intersection theory and dynamics of horizontal-like maps (2004, unknown): “Then 〈ν, ϕ〉 6 〈µ, ϕ〉 for ϕ p.s.h. on D.”
Exponential estimates for plurisubharmonic functions and stochastic dynamics (2008, unknown): “C V ] Classification AMS 2000: 32U, 37F. Keywords: Monge-Ampère measure, Green measure, exponential mixing, central limit theorem, large deviations theorem.”
Decay of correlations and the central limit theorem for meromorphic maps (2004, methodology): “n in [16, 7]. See also [26, 25, 1] for the case of projective spaces, [6] for polynomial-like maps and [15, 27, 8, 9] for the bounds of the entropy. The ddc-method that we used in diﬀerent situations [6, 7, 10, 11] leads us to precise controls of the convergence. For the maps that we consider, it al”
Pull-back of currents by holomorphic maps (2006, methodology): “Dsh currents have been introduced in [9, 12, 13].”
Green currents for holomorphic automorphisms of compact Kähler manifolds (2004, background): “Some of the results can be extended to holomorphic maps, to non singular correspondences and to birational maps [ 19 ].”
Rigidity of Julia sets for Henon type maps (2013, background): “For automorphisms of compact Kähler manifolds see Cantat, de Thélin-Dinh, Dinh-Sibony [10, 18, 26, 30, 33], for the semi-local setting of horizontal-like maps see Dinh-Nguyen-Sibony, Dujardin [23, 27, 34], for non-injective holomorphic maps see the survey [31] and the references therein.”