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Simon Hochgerner

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Related publications (5)

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Geometry of non-holonomic diffusion

Tudor Ratiu, Simon Hochgerner

We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For G-Chap ...

European Mathematical Soc2015

Symmetry Reduction Of Brownian Motion And Quantum Calogero-Moser Models

Simon Hochgerner

Let Q be a Riemannian G-manifold. This paper is concerned with the symmetry reduction of Brownian motion in Q and ramifications thereof in a Hamiltonian context. Specializing to the case of polar actions, we discuss various versions of the stochastic Hamil ...

World Scientific Publ Co Pte Ltd2013

Chaplygin systems associated to Cartan decompositions of semi-simple Lie groups

Simon Hochgerner

We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved measure and when inte ...

Elsevier2010

G-Chaplygin Systems With Internal Symmetries, Truncation, And An (Almost) Symplectic View Of Chaplygin'S Ball

Simon Hochgerner

Via compression ([18,8]) we write the n-dimensional Chaplygin sphere system as an almost Hamiltonian system on T*SO (n) with internal symmetry group SO (n-1). We show how this symmetry group can be factored out, and pass to the fully reduced system on (a f ...

2009

Stochastic Chaplygin Systems

Simon Hochgerner

We mimic the stochastic Hamiltonian reduction of Lazaro-Cami and Ortega [18, 19] for the case of certain nonholonomic systems with symmetries. ...

Elsevier2010