Dynamics of bimeromorphic maps of surfaces

By J. Diller, C. Favre. 2001

383 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e1369bd50b984ed19d2e4ddd0f8c515cdaa1fdde

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In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Energy and invariant measures for birational surface maps (2003, background): “ties follow from Theorem 2.6. The second inequality follows from continuity of π∗ acting on positive closed (1,1) currents, and the third equality is a consequence of the proof of Proposition 1.13 in [DF]. Clearly c′ >0. Proposition 2.9. Let h: X → Y be a bimeromorphic map, and let f˜ = hfh−1 be ”
Current trends and open problems in arithmetic dynamics (2018, background): “7 is known when f is a birationalm map (Diller–Favre, 2001, [57]) and when f is a polynomial map (Favre–Jonsson, 2007, [71]).”
Dynamical Degrees, Arithmetic Degrees, and Canonical Heights for Dominant Rational Self-Maps of Projective Space (2011, methodology): “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].”
Une borne supérieure pour l'entropie topologique d'une application rationnelle (2003, background): “Remarques 8. a. Russakovskii et Shiffman [16] ont montré l’inégalité δl(f ◦ g) ≤ δl(f)δl(g) lorsque X = P k. Diller et Favre [5] ont décrit précisément la croissance de δ1(f l) lorsque f est une application biméromorphe sur une surface complexe.”
Degree-growth of monomial maps (2006, background): “More recent articles on the topic of dynamical degree, intersections, and algebraic entropy include [BK], [BFJ], [ DF ], [DS], [FJ], [T1], [T2], and [TEGORS].”
Cremona transformations, surface automorphisms and plane cubics (2008, background): “Let us first describe the precise situation and manner in which a quadratic transformation f can be lifted to an automorphism on a rational surface X obtained from P 2 be a sequence of blowups (see [BK2] and [ DF ] for more on this).”
Dynamics of automorphisms of compact complex surfaces (2014, background): “11, with one more case: It may happen that dn grows linearly with n, in which case f preserves a pencil of rational curves (see [74, 49]).”
Periodic points of birational transformations on projective surfaces (2015, methodology): “generally for any birational map such that the points of indeterminacy of f−1 does not cluster too much near the points of indeterminacy of f. We refer to [3] for a precise statement. It follows from [12] that any birational map with λ1 > 1 deﬁned over a nonrational surface is birationally equiva”
Symétries birationnelles des surfaces feuilletées (2002, background): “7]. Parall`element, la dynamique des transformations holomorphes ou m´eromorphes des vari´et´es k¨ahl´eriennes, notamment des surfaces, s’est rapidement d´evelopp´ee [23], [3], [14], [29], [22], [4], [12], [10]. Cet article se place a la crois´ee de ces deux th`emes. Son but, en eﬀet, est de classer”
Invariant curves for birational surface maps (2005, background): “ as follows. Section 2 contains (mostly well-known) deﬁnitions and results concerning geometry of surfaces and birational maps on surfaces. It also reviews a classiﬁcation ofbirational self-maps from [DF] thatwe will rely onheavily. Section 3 presents, among other things, the proof of Theorem 1.1. T”
Suites d’Applications Méromorphes Multivaluées et Courants Laminaires (2005, background): “Notons que dans le cas des automorphismes du type Hénon, la laminarité de courants de Green a permis de démontrer de nombreuses propriétés dynamiques importantes (voir aussi [5, 7, 22, 14] pour le cas des applications biméromorphes sur les surfaces).”