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Filippo Bracci Manuel D. Contreras Santiago Díaz-Madrigal 《Journal d'Analyse Mathématique》2011,115(1):273-292
We show that an evolution family of the unit disc is commuting if and only if the associated Herglotz vector field has separated
variables. This is the case if and only if the evolution family comes from a semigroup of holomorphic self-maps of the disc. 相似文献
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Filippo Bracci Manuel D. Contreras Santiago Díaz-Madrigal 《Journal de Mathématiques Pures et Appliquées》2017,107(1):78-99
Let , be two one-parameter semigroups of holomorphic self-maps of the unit disk . Let be a homeomorphism. We prove that, if for all , then f extends to a homeomorphism of outside exceptional maximal contact arcs (in particular, for elliptic semigroups, f extends to a homeomorphism of ). Using this result, we study topological invariants for one-parameter semigroups of holomorphic self-maps of the unit disk. 相似文献
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Filippo Bracci Manuel D. Contreras Santiago Díaz-Madrigal 《Journal d'Analyse Mathématique》2007,102(1):119-142
We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in ℂn, n ≥ 1. For the case n = 1, we also completely describe the associated Koenigs function and solve the embedding problem from a dynamical point of
view, proving (among other things) that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear
fractional maps if and only if it contains a linear fractional map for some positive time.
Partially supported by the Ministerio de Ciencia y Tecnología and the European Union (FEDER) project BFM2003-07294-C02-02 and by La Consejería de Educación y Ciencia de la Junta de Andalucía. 相似文献
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Filippo Bracci Manuel D. Contreras Santiago Díaz-Madrigal 《Constructive Approximation》2013,37(3):357-381
We introduce the notion of regular (boundary) poles for infinitesimal generators of semigroups of holomorphic self-maps of the unit disc. We characterize such regular poles in terms of β-points (i.e., pre-images of values with positive Carleson–Makarov β-numbers) of the associated semigroup and of the associated Königs intertwining function. We also define a natural duality operation in the cone of infinitesimal generators and show that the regular poles of an infinitesimal generator correspond to the regular null poles of the dual generator. Finally we apply such a construction to study radial multi-slits and give an example of a nonisolated radial slit whose tip does not have not a positive Carleson–Makarov β-number. 相似文献
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Tiziano Casavecchia Santiago Díaz-Madrigal 《Complex Analysis and Operator Theory》2013,7(5):1457-1479
The aim of this work is to establish the celebrated Denjoy–Wolff Theorem in the context of generalized Loewner chains. In contrast with the classical situation where essentially convergence to a certain point in the closed unit disk is the unique possibility, several new dynamical phenomena appear in this framework. Indeed, ω-limits formed by suitable closed arcs of circumferences appear now as natural possibilities of asymptotic dynamical behavior. 相似文献
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Filippo Bracci Manuel D. Contreras Santiago Díaz-Madrigal 《Mathematische Annalen》2009,344(4):947-962
We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete
non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type differential equation on manifolds.
M. D. Contreras and S. Díaz-Madrigal were partially supported by the Ministerio de Ciencia e Innovación and the European Union (FEDER), project MTM2006-14449-C02-01, by La Consejería de Educación y Ciencia de la Junta de Andalucía, and by the European Science Foundation Research Networking Programme HCAA. 相似文献
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Bracci Filippo Contreras Manuel D. Díaz-Madrigal Santiago Gumenyuk Pavel 《Annali di Matematica Pura ed Applicata》2015,194(1):221-245
Annali di Matematica Pura ed Applicata (1923 -) - We characterize regular fixed points of evolution families in terms of analytical properties of the associated Herglotz vector fields and... 相似文献
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Manuel D. Contreras Santiago Díaz-Madrigal 《Journal of Mathematical Analysis and Applications》2021,493(1):124525
We prove that topological evolution families on a Riemann surface S are rather trivial unless S is conformally equivalent to the unit disc or the punctuated unit disc. We also prove that, except for the torus where there is no non-trivial continuous Loewner chain, there is a topological evolution family associated to any topological Loewner chain and, conversely, any topological evolution family comes from a topological Loewner chain on the same Riemann surface. 相似文献