6,296 research outputs found
Equidistribution towards the bifurcation current I : Multipliers and degree d polynomials
In the moduli space of degree d polynomials, the set Per\_n(w) of classes [f]
for which f admits a cycle of exact period n and multiplier w is known to be an
algebraic hypersurface. We prove that, given a complex number w, these
hypersurfaces equidistribute towards the bifurcation current as n tends to
infinity.Comment: Modified third section. Some results of Section 3 have been made more
precise. Minor errors correcte
Strong bifurcation loci of full Hausdorff dimension
In the moduli space of degree rational maps, the
bifurcation locus is the support of a closed positive current T_\bif
which is called the bifurcation current. This current gives rise to a measure
\mu_\bif:=(T_\bif)^{2d-2} whose support is the seat of strong bifurcations.
Our main result says that \supp(\mu_\bif) has maximal Hausdorff dimension
. As a consequence, the set of degree rational maps having
distinct neutral cycles is dense in a set of full Hausdorff dimension.Comment: 37 page
Continuity of the Green function in meromorphic families of polynomials
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 with a continuous error term.Comment: Modified references. Added a corollary about the adelic metric
associated with an algebraic family endowed with a marked poin
Symmetrization of Rational Maps: Arithmetic Properties and Families of Latt\`es Maps of
In this paper we study properties of endomorphisms of using a
symmetric product construction . Symmetric products have been used to produce examples of endomorphisms of
with certain characteristics, . In the present note, we
discuss the use of these maps to enlighten arithmetic phenomena and stability
phenomena in parameter spaces. In particular, we study notions of uniform
boundedness of rational preperiodic points via good reduction information,
-deep postcritically finite maps, and characterize families of Latt\`es
maps.Comment: Added more background and references; repaired a small gap in Lemma
3.1; reordered some statements in Propositions 1.1 and 1.2; 26 page
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