44 citations · 170 across the 28 of their papers we have counts for
15 papers · 1 filter
Topological entropy of a rational map over a complete metrized field
Charles Favre, Tuyen Trung Truong, Junyi Xie
We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum o…
When do two rational functions have locally biholomorphic Julia sets?
Romain Dujardin, Charles Favre, Thomas Gauthier
In this article we address the following question, whose interest was recently renewed by problems arising in arithmetic dynamics: under which conditions does there exist a local b…
The arithmetic of polynomial dynamical pairs
Charles Favre, Thomas Gauthier
We study one-dimensional algebraic families of pairs given by a polynomial with a marked point. We prove an "unlikely intersection" statement for such pairs thereby exhibiting stro…
Degenerations of SL(2,C) representations and Lyapunov exponents
Romain Dujardin, Charles Favre
We study the asymptotic behavior of the Lyapunov exponent in a meromorphic family of random products of matrices in SL(2, C), as the parameter converges to a pole. We show that the…
Continuity of the Green function in meromorphic families of polynomials
Charles Favre, Thomas Gauthier
We prove that along any marked point the Green function of a meromorphic family of polynomials parameterized by the punctured unit disk explodes exponentially fast near the origin…
Degeneration of endomorphisms of the complex projective space in the hybrid space
Charles Favre
We consider a meromorphic family of endomorphisms of degree at least 2 of a complex projective space that is parameterized by the unit disk.We prove that the measure of maximal ent…
Degree Growth of Rational Maps Induced from Algebraic Structures
Charles Favre, Jan-Li Lin
For a finite dimensional vector space equipped with a -algebra structure, one can define rational maps using the algebraic structure. In this paper, we describe the grow…
Classification of special curves in the space of cubic polynomials
Charles Favre, Thomas Gauthier
We describe all special curves in the parameter space of complex cubic polynomials, that is all algebraic irreducible curves containing infinitely many post-critically finite polyn…
Normal surface singularities admitting contracting automorphisms
Charles Favre, Matteo Ruggiero
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface a…
Distribution of postcritically finite polynomials
Charles Favre, Thomas Gauthier
We prove that Misiurewicz parameters with prescribed combinatorics and hyperbolic parameters with (d - 1) distinct attracting cycles with given multipliers are equidistributed with…
Degree growth of monomial maps and McMullen's polytope algebra
Charles Favre, Elizabeth Wulcan
We compute all dynamical degrees of monomial maps by interpreting them as mixed volumes of polytopes. By exploiting further the isomorphism between the polytope algebra of P. McMul…
Dynamical compactifications of C^2
Charles Favre, Mattias Jonsson
We find good dynamical compactifications for arbitrary polynomial mappings of C^2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula…
Degree growth of meromorphic surface maps
S. Boucksom, C. Favre, M. Jonsson
We study the degree growth of iterates of meromorphic selfmaps of compact Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show that the degrees grow simil…
Distribution of rational maps with a preperiodic critical point
Romain Dujardin, Charles Favre
Let {f_t} be any algebraic family of rational maps of a fixed degree, with a marked critical point c(t). We first prove that the hypersurfaces of parameters for which c(t) is perio…
Brolin's Theorem for curves in two complex dimensions
Charles Favre, Mattias Jonsson
Given a holomorphic selfmap f of the complex projective plane of algebraic degree at least 2, we give sufficient conditions on a positive closed (1,1) current S of unit mass under…