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The Lie Group Structure of the Butcher Group
TLDR
The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge–Kutta methods. Expand
The Lie group of bisections of a Lie groupoid
In this article, we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebraExpand
Extending Whitney's extension theorem: nonlinear function spaces
This article shows that there is a continuous extension operator for compactly-supported smooth sections of vector bundles on possibly non-compact smooth manifolds, where the closed set to whichExpand
Lie groupoids of mappings taking values in a Lie groupoid
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These areExpand
The Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if itExpand
Lie groups of controlled characters of combinatorial Hopf algebras
In this article groups of controlled characters of a combinatorial Hopf algebra are considered from the perspective of infinite-dimensional Lie theory. A character is controlled in our sense if itExpand
Character groups of Hopf algebras as infinite-dimensional Lie groups
In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we construct an infinite-dimensional LieExpand
Differentiable mappings on products with different degrees of differentiability in the two factors
Abstract We develop differential calculus of C r , s -mappings on products of locally convex spaces and prove exponential laws for such mappings. As an application, we consider differential equationsExpand
STRONG TOPOLOGIES FOR SPACES OF SMOOTH MAPS WITH INFINITE-DIMENSIONAL TARGET
In this article we study two "strong" topologies for spaces of smooth functions from a finite-dimensional manifold to a (possibly infinite-dimensional) manifold modeled on a locally convex space.Expand
Shape Analysis on Homogeneous Spaces: A Generalised SRVT Framework
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compareExpand
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