13,046 research outputs found
Diagonalization of non-diagonalizable discrete holomorphic dynamical systems
We describe a canonical procedure for associating to any (germ of)
holomorphic self-map f of C^n fixing the origin such that df_O is invertible
and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p
from M to C^n, a point e in M and a (germ of) holomorphic self-map F of M so
that: p restricted to the complement of p^{-1}(O) is a biholomorphism between
this complement and C^n minus the origin; p semiconjugates f and F; and e is a
fixed point of F such that dF_e is diagonalizable. Furthermore, we use this
construction to describe the local dynamics of such an f nearby the origin when
the only eigenvalue of df_O is 1.Comment: Plain-TeX file, 17 page
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Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains
We characterize using the Bergman kernel Carleson measures of Bergman spaces
in strongly pseudoconvex bounded domains in several complex variables,
generalizing to this setting theorems proved by Duren and Weir for the unit
ball. We also show that uniformly discrete (with respect to the Kobayashi
distance) sequences give examples of Carleson measures, and we compute the
speed of escape to the boundary of uniformly discrete sequences in strongly
pseudoconvex domains, generalizing results obtained in the unit ball by
Jevti\'c, Massaneda and Thomas, by Duren and Weir, and by MacCluer.Comment: 17 page
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