5 citations · 12 across the 12 of their papers we have counts for
15 papers
Strong Legendre regularity and short-time analysis of abnormal curves
Francesco Boarotto
We study strictly abnormal sub-Riemannian extremals satisfying the Goh condition and a strong (i.e., coercive) generalized Legendre condition, imposed only at the Lebesgue points o…
The Sard problem in step 2 and in filiform Carnot groups
Francesco Boarotto, Luca Nalon, Davide Vittone
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 (de…
Higher order Goh conditions for singular extremals of corank 1
Francesco Boarotto, Roberto Monti, Alessandro Socionovo
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 ma…
On the Lebesgue measure of the boundary of the evoluted set
Francesco Boarotto, Laura Caravenna, Francesco Rossi +1
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…
Fuller singularities for generic control-affine systems with an even number of controls
Francesco Boarotto, Yacine Chitour, Mario Sigalotti
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…
A dynamical approach to the Sard problem in Carnot groups
Francesco Boarotto, Davide Vittone
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 trajector…
Third order open mapping theorems and applications to the end-point map
Francesco Boarotto, Roberto Monti, Francesco Palmurella
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 fi…
Dwell-time control sets and applications to the stability analysis of linear switched systems
Francesco Boarotto, Mario Sigalotti
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,…
Structure of the endpoint map near nice singular curves
Andrei A. Agrachev, Francesco Boarotto
Given a rank-two sub-Riemannian structure and a point , a singular curve is a critical point of the endpoint map defined on the space of horizont…
Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature
Davide Barilari, Francesco Boarotto
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 coeffi…
Time-Optimal Trajectories of Generic Control-Affine Systems Have at Worst Iterated Fuller Singularities
Francesco Boarotto, Mario Sigalotti
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 con…
On the set of points of smoothness for the value function for affine optimal control problems
Davide Barilari, Francesco Boarotto
We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial…
Homotopically Invisible Singular Curves
Andrei A. Agrachev, Francesco Boarotto, Antonio Lerario
Given a smooth manifold and a totally nonholonomic distribution of rank , we study the effect of singular curves on the topology of the space of horizontal pat…
Homotopy properties of endpoint maps and a theorem of Serre in subriemannian geometry
Francesco Boarotto, Antonio Lerario
We discuss homotopy properties of endpoint maps for affine control systems. We prove that these maps are Hurewicz fibrations with respect to some topology on the space of…
Conformal equivalence of sub-Riemannian 3D contact structures on Lie groups
Francesco Boarotto
In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy:…