Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Boarotto, Francesco"'
We study the Sard problem for the endpoint map in some well-known classes of Carnot groups. Our first main result deals with step 2 Carnot groups, where we provide lower bounds (depending only on the algebra of the group) on the codimension of the ab
Externí odkaz:
http://arxiv.org/abs/2203.16360
We prove Goh conditions of order n for strictly singular length minimizing curves of corank 1, under the assumption that the lower order intrinsic differentials of the end-point map vanish. This result relies upon the proof of an open mapping theorem
Externí odkaz:
http://arxiv.org/abs/2202.00300
Publikováno v:
Systems & Control Letters, Volume 158, 2021
The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the evoluted set has negligible boundary (i.e. its Lebes
Externí odkaz:
http://arxiv.org/abs/2107.06739
In this article we study how bad can be the singularities of a time-optimal trajectory of a generic control affine system. In the case where the control is scalar and belongs to a closed interval it was recently shown in [6] that singularities cannot
Externí odkaz:
http://arxiv.org/abs/1909.01061
Autor:
Boarotto, Francesco, Vittone, Davide
We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an applications, we positively a
Externí odkaz:
http://arxiv.org/abs/1908.11120
Publikováno v:
Nonlinearity, 33 (2020), 4539-4567
This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a finite dimensional manifold. In a second step, we compute the third orde
Externí odkaz:
http://arxiv.org/abs/1907.11016
Autor:
Boarotto, Francesco, Sigalotti, Mario
We propose an extension of the theory of control sets to the case of inputs satisfying a dwell-time constraint. Although the class of such inputs is not closed under concatenation, we propose a suitably modified definition of control sets that allows
Externí odkaz:
http://arxiv.org/abs/1902.03757
Given a rank-two sub-Riemannian structure $(M,\Delta)$ and a point $x_0\in M$, a singular curve is a critical point of the endpoint map $F:\gamma\mapsto\gamma(1)$ defined on the space of horizontal curves starting at $x_0$. The typical least degenera
Externí odkaz:
http://arxiv.org/abs/1810.12662
Autor:
Barilari, Davide, Boarotto, Francesco
We consider the heat equation associated with a class of hypoelliptic operators of Kolmogorov-Fokker-Planck type in dimension two. We explicitly compute the first meaningful coefficient of the small time asymptotic expansion of the heat kernel on the
Externí odkaz:
http://arxiv.org/abs/1709.08588
Autor:
Boarotto, Francesco, Sigalotti, Mario
We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u as
Externí odkaz:
http://arxiv.org/abs/1705.10055