We present a set-oriented graph-based framework for continuous-time optimal transport over nonlinear dynamical systems. Our approach allows us to recover provably optimal control laws for steering a given initial distribution in phase space to a final distribution in prescribed finite time for the case of nonlinear control-affine systems. The action of the controlled vector fields is approximat...

In this paper, we study differential forms and vector fields on the orbit space of a proper action Lie group smooth manifold, defining them as multilinear maps generators infinitesimal diffeomorphisms, respectively. This yields an intrinsic view space.

The goal of this work is to introduce the two-parameter conformable fractional semigroups and provide a definition its infinitesimal generator. For such generators, we develop multiple results. In addition, show that solution for abstract Cauchy problems.

This paper is a continuation of the works by Fukushima-Tanaka [14] and Chen-FukushimaYing [8] on the study of one-point extendability of a pair of standard Markov processes in weak duality. In this paper, general conditions to ensure such an extension are given. In the symmetric case, characterizations of the one-point extensions are given in terms of their Dirichlet forms and in terms of their...

Rather general results are obtained for determining the nature of infinitesimal generators which can be admitted by a given differential equation. Simple criteria are given to determine whether or not (1) the infinitesimals of independent variables can depend only on independent variables and (2) the infinitesimal of the dependent variable can depend at most linearly on the dependent variable. ...

With every Lie semi-group, Π, possessing certain regularity properties, there is associated a Lie algebra, A; and with every strongly continuous representation of Π in a Banach space there is associated a representation A(a) of A. Certain theorems regarding this representation are established. The above theorems are valid for a representation of a Lie group also. In this case, it is shown that ...

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, i.e., at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point...

By using Bernstein functions, existence and concentration properties are studied for invariant measures of the infinitesimal generators associated to a large class of stochastic generalized porous media equations. In particular, results derived in [4] are extended to equations with non-constant and stronger noises. Analogous results are also proved for invariant probability measures for strong ...