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

Small holder farmers’ experience on pressurized irrigation systems in Kobo Valley

Irrigation systemsFarmers attitudes

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