Une borne supérieure pour l'entropie topologique d'une application rationnelle

By T. Dinh, N. Sibony. 2003

230 citations recorded by the source corpus.

Let X be a complex projective manifold and let f be a dominating rational map from X onto X. We show that the topological entropy h(f) of f is bounded from above by the logarithm of its maximal dynamical degree.

Subfields: Analytical Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/72d42fbba0abc42cc8db8f9a55690c4b2d45bfc7

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In Analytical Chemistry

In Mathematical Physics

Citations in the corpus

Degrees of iterates of rational maps on normal projective varieties (2017, methodology): “When K = C, Theorem 1 was proved by Dinh and Sibony in [11], and further generalized to compact Kähler manifolds in [10].”
Distribution des valeurs de transformations méromorphes et applications (2006, background): “Dans ce cas, la suite [λs(f)] converge vers sa borne inférieure infn≥1[λs(f n)]1/n (voir [9]).”
Comparison of dynamical degrees for semi-conjugate meromorphic maps (2009, background): “The dynamical degree dp(f) of order p is the quantity which measures the growth of the norms of (fn)∗ acting on the Hodge cohomology group Hp,p(X,R) when n tends to infinity.”
Regularization of currents and entropy (2004, background): “We deduce from this theorem the following corollary which is proved in [10] for projective manifolds.”
Dynamical Degrees, Arithmetic Degrees, and Canonical Heights for Dominant Rational Self-Maps of Projective Space (2011, background): “Dynamical degrees were initially studied by Russakovskii and Shiffman [53] and Arnol′d [5] in the 1990s, and they have since attracted considerable attention; see for example [8, 10, 11, 18, 22, 23, 24, 26, 33, 44, 43, 45, 47, 61].”
Relative dynamical degrees of correspondences over a field of arbitrary characteristic (2016, result): “In another direction, when K = C, Dinh and Sibony [11] defined dynamical degrees and topological entropy for meromorphic correspondences over irreducible varieties.”
Dynamical degrees of birational transformations of projective surfaces (2013, background): “For instance, if k is the field of complex numbers, log(λ( f )) provides an upper bound for the topological entropy of f : X(C) 99K X(C) and is equal to it under natural assumptions (see [3, 21]).”