arXiv subjects

Fabiano B. da Silva

Publications and source records attributed to Fabiano B. da Silva.

2 recordsLinked to original sources

arXiv2012

Decomposition of stochastic flows in manifolds with complementary distributions

Let $M$ be a differentiable manifold endowed locally with two complementary distributions, say horizontal and vertical. We consider the two subgroups of (local) diffeomorphisms of $M$ generated by vector fields in each of of these distributions. Given a stochastic flow $φ_t$ of diffeomorphisms of $M$, in a neighbourhood of initial condition, up to a stopping time we decompose $φ_t = ξ_t \circ ψ_t$ where the first component is a diffusion in the group of horizontal diffeomorphisms and the second component is a process in the group of vertical diffeomorphisms. Further decomposition will include more than two components; it leads to a maximal cascade decomposition in local coordinates where each component acts only in the corresponding coordinate.

math.DS↗

arXiv2011

Decomposition of stochastic flows with automorphism of subbundles component

We show that given a $G$-structure $P$ on a differentiable manifold $M$, if the group $G(M)$ of automorphisms of $P$ is big enough, then there exists the quotient of an stochastic flows $phi_t$ by $G(M)$, in the sense that $ϕ_t = ξ_t \circ ρ_t$ where $ξ_t \in G(M)$, the remainder $ρ_t$ has derivative which is vertical but transversal to the fibre of $P$. This geometrical context generalizes previous results where $M$ is a Riemannian manifold and $ϕ_t$ is decomposed with an isometric component, see Liao \cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds to the particular case of an SO(n)-structure on $M$.

math.DS↗