# Analytic Diffeomorphism

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### Michael P. Cohen – One of the best experts on this subject based on the ideXlab platform.

• ##### Some applications of Hölder’s theorem in groups of AnalyticDiffeomorphisms of 1-manifolds
, 2015
Co-Authors: Azer Akhmedov, Michael P. Cohen

Abstract:

ABSTRACT: We obtain a simple obstruction to embedding groups into the Analytic Diffeomorphism groups of 1-manifolds. Using this, we classify all RAAGs which embed into Diffω+(S1). We also prove that a branch group does not embed into Diffω+(S1). 1

• ##### Some applications of Hölder’s theorem in groups of AnalyticDiffeomorphisms of 1-manifolds
Topology and its Applications, 2015
Co-Authors: Azer Akhmedov, Michael P. Cohen

Abstract:

Abstract We obtain a simple obstruction to embedding groups into the Analytic Diffeomorphism groups of 1-manifolds. Using this, we classify all RAAGs which embed into Diff + ω ( S 1 ) . We also prove that a branch group does not embed into Diff + ω ( S 1 ) .

• ##### Some applications of H\”older’s theorem in groups of AnalyticDiffeomorphisms of 1-manifolds
arXiv: Group Theory, 2014
Co-Authors: Azer Akhmedov, Michael P. Cohen

Abstract:

We obtain a simple obstruction to embedding groups into the Analytic Diffeomorphism groups of 1-manifolds. Using this, we classify all RAAGs which embed into $\mathrm{Diff}_{+}^{\omega }(\mathbb{S}^1)$. We also prove that a branch group does not embed into $\mathrm{Diff}_{+}^{\omega }(\mathbb{S}^1)$.

### Helge Glöckner – One of the best experts on this subject based on the ideXlab platform.

• ##### Invariant manifolds for finite-dimensional non-archimedean dynamical systems
arXiv: Dynamical Systems, 2014
Co-Authors: Helge Glöckner

Abstract:

Let M be an Analytic manifold modelled on an ultrametric Banach space over a complete ultrametric field. Let f be an Analytic Diffeomorphism from M onto itself and p be a fixed point of f. We discuss invariant manifolds around p, like stable manifolds, centre-stable manifolds and centre manifolds, with an emphasis on results specific to the case that M has finite dimension. The results have applications in the theory of Lie groups over totally disconnected local fields.

• ##### Invariant manifolds for Analytic dynamical systems over ultrametric fields
Expositiones Mathematicae, 2013
Co-Authors: Helge Glöckner

Abstract:

Abstract We give an exposition of the theory of invariant manifolds around a fixed point, in the case of time-discrete, Analytic dynamical systems over a complete ultrametric field K . Typically, we consider an Analytic manifold M modelled on an ultrametric Banach space over K , an Analytic Diffeomorphism f : M → M , and a fixed point p of f . Under suitable assumptions on the tangent map T p ( f ) , we construct a centre–stable manifold, a centre manifold, respectively, an a -stable manifold around  p , for a given real number a ∈ ] 0 , 1 ] .

### James A. Vickers – One of the best experts on this subject based on the ideXlab platform.

• ##### The Hausdorff Dimension of Exceptional Sets Associated with Normal Forms
Journal of the London Mathematical Society, 1994
Co-Authors: M. M. Dodson, Bryan P. Rynne, James A. Vickers

Abstract:

The Hausdorff dimension is obtained for exceptional sets associated with linearising a complex Analytic Diffeomorphism near a fixed point, and for related exceptional sets associated with obtaining a normal form of an Analytic vector field near a singular point. The exceptional sets consist of eigenvalues which do not satisfy a certain Diophantine condition and are ‘close’ to resonance. They are related to ‘lim-sup’ sets of a general type arising in the theory of metric Diophantine approximation and for which a lower bound for the Hausdorff dimension has been obtained.