Equidistribution towards the bifurcation current I : Multipliers and degree d polynomials
نویسنده
چکیده
— In the moduli space Pd of degree d polynomials, the set Pern(w) of classes [f ] for which f admits a cycle of exact period n and multiplier multiplier w is known to be an algebraic hypersurface. We prove that, given w ∈ C, these hypersurfaces equidistribute towards the bifurcation current as n tends to infinity.
منابع مشابه
The Dynamical André-oort Conjecture: Unicritical Polynomials
We establish the equidistribution with respect to the bifurcation measure of postcritically finite maps in any one-dimensional algebraic family of unicritical polynomials. Using this equidistribution result, together with a combinatorial analysis of certain algebraic correspondences on the complement of the Mandelbrot set M2 (or generalized Mandelbrot set Md for degree d > 2), we classify all c...
متن کاملQuadratic polynomials, multipliers and equidistribution
Given a sequence of complex numbers ρn, we study the asymptotic distribution of the sets of parameters c ∈ C such that the quadratic maps z2+c has a cycle of period n and multiplier ρn. Assume 1 n log |ρn| → L. If L ≤ log 2, they equidistribute on the boundary of the Mandelbrot set. If L > log 2 they equidistribute on the equipotential of the Mandelbrot set of level 2L− 2 log 2. Introduction In...
متن کاملEquidistribution of Rational Functions Having a Superattracting Periodic Point towards the Activity Current and the Bifurcation Current
We establish an approximation of the activity current Tc in the parameter space of a holomorphic family f of rational functions having a marked critical point c by parameters for which c is periodic under f , i.e., is a superattracting periodic point. This partly generalizes a Dujardin–Favre theorem for rational functions having preperiodic points, and refines a Bassanelli–Berteloot theorem on ...
متن کاملDynamics of Rational Maps: a Current on the Bifurcation Locus
Let fλ : P 1 → P be a family of rational maps of degree d > 1, parametrized holomorphically by λ in a complex manifold X. We show that there exists a canonical closed, positive (1,1)-current T on X supported exactly on the bifurcation locus B(f) ⊂ X. If X is a Stein manifold, then the stable regime X − B(f) is also Stein. In particular, each stable component in the space Polyd (or Ratd) of all ...
متن کاملHarmonic theta series and equidistribution
is a holomorphic modular form of weight 4 for the subgroup [1] Γθ, from the fact that there are no weight 4 cuspforms for Γθ, and from explicit computation of the Fourier coefficients of the two types of weight 4 Eisenstein series for Γθ. Toward a less frivolous result, recall that the irreducibility of spaces Hd of homogeneous, degree d harmonic polynomials f on R as O(n)-spaces gives Hecke’s ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016