Search results for " Mathematica"

Equilibrium measures for uniformly quasiregular dynamics

2012

We establish the existence and fundamental properties of the equilibrium measure in uniformly quasiregular dynamics. We show that a uniformly quasiregular endomorphism $f$ of degree at least 2 on a closed Riemannian manifold admits an equilibrium measure $\mu_f$, which is balanced and invariant under $f$ and non-atomic, and whose support agrees with the Julia set of $f$. Furthermore we show that $f$ is strongly mixing with respect to the measure $\mu_f$. We also characterize the measure $\mu_f$ using an approximation property by iterated pullbacks of points under $f$ up to a set of exceptional initial points of Hausdorff dimension at most $n-1$. These dynamical mixing and approximation resu…

The snail lemma for internal groupoids

2019

Abstract We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizers.

Irreducible induction and nilpotent subgroups in finite groups

2019

Suppose that $G$ is a finite group and $H$ is a nilpotent subgroup of $G$. If a character of $H$ induces an irreducible character of $G$, then the generalized Fitting subgroup of $G$ is nilpotent.

Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples

2016

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq 0$. This example contradicts a conjecture in \cite{HHU}. The main idea is to consider a well-understood time-$t$ map of a non-transitive Anosov flow and then carefully compose with a Dehn twist.

Stability conditions and related filtrations for $(G,h)$-constellations

2017

Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the $\theta$-stability defined for quiver representations by King and for $G$-constellations by Craw and Ishii, but depending on infinitely many parameters. The second one comes from Geometric Invariant Theory in the construction of a moduli space for $(G,h)$-constellations, and depends on some finite subset $D$ of the isomorphy classes of irreducible representations of $G$. We show that these two stability notions do not coincide, answering negatively a question raise…

2-Potenzen der ordnung von Einheitengruppen unimodularer definiter ?-Gitter

1990

Holomorphic Maps and Pencils of Circles

2008

(2008). Holomorphic Maps and Pencils of Circles. The American Mathematical Monthly: Vol. 115, No. 8, pp. 690-700.

The Composition Operation on Spaces of Holomorphic Mappings

2020

AbstractWe discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.

Rigidity of commutators and elementary operators on Calkin algebras

1998

LetA=(A 1,...,A n ),B=(B 1,...,B n )eL(l p ) n be arbitraryn-tuples of bounded linear operators on (l p ), with 1<p<∞. The paper establishes strong rigidity properties of the corresponding elementary operators e a,b on the Calkin algebraC(l p )≡L(l p )/K(l p ); $$\varepsilon _{\alpha ,b} (s) = \sum\limits_{i = 1}^n {a_i sb_i } $$ , where quotient elements are denoted bys=S+K(l p ) forSeL(l p ). It is shown among other results that the kernel Ker(e a,b ) is a non-separable subspace ofC(l p ) whenever e a,b fails to be one-one, while the quotient $$C(\ell ^p )/\overline {\operatorname{Im} \left( {\varepsilon _{\alpha ,b} } \right)} $$ is non-separable whenever e a,b fails to be onto. These re…

On Serrin’s overdetermined problem in space forms

2018

We consider Serrin’s overdetermined problem for the equation $$\Delta v + nK v = -\,1$$ in space forms, where K is the curvature of the space, and we prove a symmetry result by using a P-function approach. Our approach generalizes the one introduced by Weinberger to space forms and, as in the Euclidean case, it provides a short proof of the symmetry result which does not make use of the method of moving planes.