منابع مشابه
Limits in differential fields of holomorphic germs
Differential fields of germs of continuous real valued functions of one real variable (Hardy fields) have the property that all elements have limits in the extended real numbers and thus have a canonical valuation. For differential fields of holomorphic germs this is not generally the case. We provide a criterion for differential fields of holomorphic germs for its elements to have uniform limi...
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Let M be a two dimensional complex manifold, p ∈ M and F a germ of holomorphic foliation of M at p. Let S ⊂ M be a germ of an irreducible, possibly singular, curve at p in M which is a separatrix for F . We prove that if the Camacho-Sad-Suwa index Ind(F , S, p) 6∈ Q ∪ {0} then there exists another separatrix for F at p. A similar result is proved for the existence of parabolic curves for germs ...
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In [GP], Gambaudo and Pécou introduced the “linking property” to study the dynamics of germs of planar homeomorphims and provide a new proof of Naishul theorem. In this paper we prove that the negation of Gambaudo-Pécou property characterises the topological dynamics of holomorphic parabolic germs. As a consequence, a rotation set for germs of surface homeomorphisms around a fixed point can be ...
متن کاملHolomorphic Motions, Fatou Linearization, and Quasiconformal Rigidity for Parabolic Germs
By applying holomorphic motions, we prove that a parabolic germ is quasiconformal rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near conformal as long as we consider these germs defined on smaller and smaller neighborhoods. Before to prove this theorem, we use the idea of holomorphic motions to ...
متن کاملThe Fréchet space of holomorphic functions on the unit disc
If X is a topological space and p ∈ X, a local basis at p is a set B of open neighborhoods of p such that if U is an open neighborhood of p then there is some U0 ∈ B that is contained in U . We emphasize that to say that a topological vector space (X, τ) is normable is to say not just that there is a norm on the vector space X, but moreover that the topology τ is induced by the norm. A topologi...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1995-1219730-5