Manuel D. Contreras

activity

20062023

most citedHolomorphic self-maps of the disk intertwining two linear fractional maps

21 citations · 89 across the 25 of their papers we have counts for

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25 papers · 1 filter

math.CV2023

On the uniform convergence of continuous semigroups

Manuel D. Contreras, Carlos Gómez-Cabello, Luis Rodríguez-Piazza

Let $Ω$ be a region in the complex plane $C$ and let ${Φ_{t}}_{t \geq 0}$ be a continuous semigroup of functions on $Ω$ ; that is, $Φ_{t} : Ω \to Ω$ is holomorphic for every $t\ge…

math.CV2020

Angular extents and trajectory slopes in the theory of holomorphic semigroups in the unit disk

Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk

We study relationships between the asymptotic behaviour of a non-elliptic semigroup of holomorphic self-maps of the unit disk and the geometry of its planar domain (the image of th…

math.CV2020

Infinitesimal generators of semigroups with prescribed boundary fixed points

Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk

We study infinitesimal generators of one-parameter semigroups in the unit disk $D$ having prescribed boundary regular fixed points. Using an explicit representation of such…

math.CV2018

Asymptotic behavior of orbits of holomorphic semigroups

Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal +2

Let $(ϕ_{t})$ be a holomorphic semigroup of the unit disc (i.e., the flow of a semicomplete holomorphic vector field) without fixed points in the unit disc and let $Ω$ be the starlik…

math.CV2018

A characterization of orthogonal convergence in simply connected domains

Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal +1

Let $D$ be the unit disc in $C$ and let $f : D \to C$ be a Riemann map, $Δ = f (D)$ . We give a necessary and sufficient condition in terms of hyp…

math.CV2018

On the Königs function of semigroups of holomorphic self-maps of the unit disc

Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal

Let $(ϕ_{t})$ be a semigroup of holomorphic self-maps of~ $D$ . In this note, we use an abstract approach to define the Königs function of $(ϕ_{t})$ and "holomorphic models" and…

math.CV2018

Backward orbits and petals of semigroups of holomorphic self-maps of the unit disc

Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal +1

We study the backward invariant set of one-parameter semigroups of holomorphic self-maps of the unit disc. Such a set is foliated in maximal invariant curves and its open connected…

math.CV2018★ 6 cited

Non-tangential limits and the slope of trajectories of holomorphic semigroups of the unit disc

Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal +1

Let $Δ ⊊ C$ be a simply connected domain, let $f : D \to Δ$ be a Riemann map and let ${z_{k}} \subset Δ$ be a compactly divergent sequence. Using Gromov's hype…

math.CV2015★ 1 cited

Topological invariants for semigroups of holomorphic self-maps of the unit disc

Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal

Let $(φ_{t})$ , $(ϕ_{t})$ be two one-parameter semigroups of holomorphic self-maps of the unit disc $D \subset C$ . Let $f : D \to D$ be a homeomorphism. We…

math.CV2014

Slope problem for trajectories of holomorphic semigroups in the unit disc

Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk

It has been an open problem for about ten years whether every trajectory of a parabolic one-parameter semigroup in the unit disk tends to the Denjoy-Wolff point with a definite (an…

math.CV2013

Classical and stochastic Löwner-Kufarev equations

Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal +1

In this paper we present a historical and scientific account of the development of the theory of the Löwner-Kufarev classical and stochastic equations spanning the 90-year period f…

math.CV2013

Boundary regular fixed points in Loewner theory

Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal +1

We characterize regular fixed points of evolution families in terms of analytical properties of the associated Herglotz vector fields and geometrical properties of the associated L…

math.CV2012★ 16 cited

Local duality in Loewner equations

Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk

Among diversity of frameworks and constructions introduced in Loewner Theory by different authors, one can distinguish two closely related but still different ways of reasoning, wh…

math.CV2012

Regular poles and $β$ -numbers in the theory of holomorphic semigroups

Filippo Bracci, Manuel D. Contreras, S. Diaz-Madrigal

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 term…

math.CV2011

Loewner Theory in annulus II: Loewner chains

Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk

Loewner Theory, based on dynamical viewpoint, proved itself to be a powerful tool in Complex Analysis and its applications. Recently Bracci et al [Bracci et al, to appear in J. Rei…

math.CV2010★ 2 cited

Loewner Theory in annulus I: evolution families and differential equations

Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk

Loewner Theory, based on dynamical viewpoint, is a powerful tool in Complex Analysis, which plays a crucial role in such important achievements as the proof of famous Bieberbach's…

math.CV2010★ 1 cited

Geometry behind chordal Loewner chains

Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk

Loewner Theory is a deep technique in Complex Analysis affording a basis for many further important developments such as the proof of famous Bieberbach's conjecture and well-celebr…

math.CV2009

Semigroups versus evolution families in the Loewner theory

Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal

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 evol…

math.CV2009★ 3 cited

Loewner chains in the unit disk

Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk

In this paper we introduce a general version of the notion of Loewner chains which comes from the new and unified treatment, given in [arXiv:0807.1594], of the radial and chordal v…

math.CV2008★ 1 cited

Evolution Families and the Loewner Equation II: complex hyperbolic manifolds

Filippo Bracci, Manuel D. Contreras, S. Diaz-Madrigal

We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, provi…

math.CV2008★ 21 cited

Evolution Families and the Loewner Equation I: The Unit Disc

Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal

In this paper we introduce a general version of the Loewner differential equation which allows us to present a new and unified treatment of both the radial equation introduced in 1…

math.CV2007★ 10 cited

Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc

Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal

In this paper we prove a formula describing the infinitesimal generator of a continuous semigroup $(\v_t)$ of holomorphic self-maps of the unit disc with respect to a boundary regu…

math.CV2007

Digons and angular derivatives of analytic self-maps of the unit disk

Manuel D. Contreras, Santiago Díaz-Madrigal, Alexander Vasil'ev

We present a geometric approach to a well-known sharp inequality, due to Cowen and Pommerenke, about angular derivatives of general univalent self-maps of the unit disk.

math.CV2006

Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains

Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal

We characterize infinitesimal generators of semigroups of holomorphic self-maps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel…

On the uniform convergence of continuous semigroups

Angular extents and trajectory slopes in the theory of holomorphic semigroups in the unit disk

Infinitesimal generators of semigroups with prescribed boundary fixed points

Asymptotic behavior of orbits of holomorphic semigroups

A characterization of orthogonal convergence in simply connected domains

On the Königs function of semigroups of holomorphic self-maps of the unit disc

Backward orbits and petals of semigroups of holomorphic self-maps of the unit disc

Non-tangential limits and the slope of trajectories of holomorphic semigroups of the unit disc

Topological invariants for semigroups of holomorphic self-maps of the unit disc

Slope problem for trajectories of holomorphic semigroups in the unit disc

Classical and stochastic Löwner-Kufarev equations

Boundary regular fixed points in Loewner theory

Local duality in Loewner equations

Regular poles and β-numbers in the theory of holomorphic semigroups

Loewner Theory in annulus II: Loewner chains

Loewner Theory in annulus I: evolution families and differential equations

Geometry behind chordal Loewner chains

Semigroups versus evolution families in the Loewner theory

Loewner chains in the unit disk

Evolution Families and the Loewner Equation II: complex hyperbolic manifolds

Evolution Families and the Loewner Equation I: The Unit Disc

Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc

Digons and angular derivatives of analytic self-maps of the unit disk

Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains

Regular poles and $β$ -numbers in the theory of holomorphic semigroups