Dynamics on blowups of the projective plane

By Curtis T. McMullen. 2007

167 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6832689417102eed780acec3d050595061f23339

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Rigidity of Julia sets for Henon type maps (2013, background): “This is the case for basins of attracting points, see [48] for examples and [50] for a related result.”
Dynamics of automorphisms of compact complex surfaces (2014, methodology): “Results from Diophantine approximation imply that products like αkβl are not well approximated by roots of 1, so that Siegel’s linearization Theorem can be applied (see [101, 102]): In a neighborhood of the fixed point q, f̂ is conjugate to its linear part D f̂q; this neighborhood is therefore conta”
Dynamics of automorphisms on projective complex manifolds (2008, background): “Since L is an integral lattice of signature (1, r) and g∗|L is an isometry of L, by the proof of McMullen [36] Theorem 3.2, d1 is a Salem number and all eigenvalues of g ∗|L are given as: d1, d −1 1 , α1, ᾱ1, . . . , αt, ᾱt with |αi| = 1 and 2(t + 1) = r + 1.”
Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy (2013, background): “m. Complex dynamics of biholomorphic automorphisms of compact Ka¨hler surfaces is now fairly well-understood since Cantat [Ca99]. Especially, BedfordKim ([BK09], [BK12], [BK10]) and McMullen ([Mc02], [Mc07], [Mc11], [Mc13]) show very beautiful aspects of automorphisms of rational surfaces and K3 sur”
Continuous families of rational surface automorphisms with positive entropy (2008, background): “Indeed, the first infinite family of such rational surfaces was found only recently (see [1,2] and [10]).”
The diminished base locus is not always closed (2012, methodology): “This was studied in dimension 2 in the work of McMullen [13] and Bedford-Kim [2],[3], and in higher dimension by PerroniZhang [17].”
Rational Surface Automorphisms with Positive Entropy (2010, background): “I am grateful to Professor TOME 66 (2016), FASCICULE 1 432 Takato UEHARA Eric Bedford, Professor Julie Deserti, Professor Jeffrey Diller, Professor Charles Favre and Professor Curtis T. McMullen for useful advices, and to Professor Yutaka Ishii, Professor Eiichi Sato and Professor Mitsuhiro Shishiku”
Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences (2006, methodology): “1) of [4] for the birational family; [20] changed this notation to (x, y) → (y, y/x) + (α,β), which is conjugate to fa,b if α = b − a and β = a.”
Dynamical degrees of birational transformations of projective surfaces (2013, background): “Once Theorem A is proved, three corollaries can be deduced from results of McMullen and the second author (see [37] and [16]).”
Cremona transformations, surface automorphisms and plane cubics (2008, methodology): “4 This fortunate coincidence is largely accounted for in §7 of [McM] whose arguments show that the multiplier a for a tentative realization must be a root of P(λ) and conversely that each root of P(λ), disregarding multiplicity, gives rise to at least one tentative realization.”
Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups (2011, background): “.2. Wehler varieties. Coxeter groups also appear in the theory of algebraic surfaces, mostly as hyperbolic reﬂection groups acting on N éron-Severi groups (see for instance [Ni], [Bor], [CaDo], [Do], [Mc2], [To]). Let n be a positive integer. Let X be a smooth complex hypersurface of (P1)n+1. The ad”
Rational surfaces with a large group of automorphisms (2011, background): “There are classical examples of this kind as well as very recent constructions (see [20], [3], [31], [40]).”