Abstract. We discuss homotopy properties of endpoint maps for affine control systems. We prove that these maps are Hurewicz fibrations with respect to some W 1,p topology on the space of trajectories, for a certain p> 1. We study critical points of geometric costs for these affine control systems, proving that if the base manifold is compact then the number of their critical points is infinite (we use Lusternik-Schnirelmann category combined with the Hurewicz property). In the special case where the control system is subriemannian this result can be read as the corresponding version of Serre’s theorem, on the existence of infinitely many geodesics between two points on a compact riemannian manifold. In the subriemannian case we show that...
65 pages. We generalized the results in the first version and add an appendix in collaboration with ...
We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along su...
In this letter we present a decomposition for control systems whose drift vector field is the geod...
We discuss homotopy properties of endpoint maps for affine control systems. We prove that these maps...
Abstract. Given a manifold M and a proper sub-bundle ∆ ⊂ TM, we study homotopy properties of the ho...
Given a manifold $M$ and a proper sub-bundle $\Delta\subset TM$, we study homotopy properties of the...
AbstractThis paper considers monotonic (or causal) homotopy between trajectories of control systems....
AbstractWe prove that a proper map f : Mm → Nn between manifolds is a Serre fibration if it has the ...
Several recent investigations have focused attention on spaces and manifolds which are non-compact b...
One of the fundamental problems in control theory is that of controllability, the question of whethe...
In this paper we prove that for a restricted affine control system on a connected manifold M, the as...
From a topological point of vien this work deals with the structure of a set of affine and controlla...
We prove the following theorem. Let f be a dominant endomorphism of a projective surface over an alg...
AbstractWe give a topological characterization of ω-limit sets of continuous antitriangular maps, th...
In this thesis, we are studying topological and dynamical conditions imposing infinitely many period...
65 pages. We generalized the results in the first version and add an appendix in collaboration with ...
We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along su...
In this letter we present a decomposition for control systems whose drift vector field is the geod...
We discuss homotopy properties of endpoint maps for affine control systems. We prove that these maps...
Abstract. Given a manifold M and a proper sub-bundle ∆ ⊂ TM, we study homotopy properties of the ho...
Given a manifold $M$ and a proper sub-bundle $\Delta\subset TM$, we study homotopy properties of the...
AbstractThis paper considers monotonic (or causal) homotopy between trajectories of control systems....
AbstractWe prove that a proper map f : Mm → Nn between manifolds is a Serre fibration if it has the ...
Several recent investigations have focused attention on spaces and manifolds which are non-compact b...
One of the fundamental problems in control theory is that of controllability, the question of whethe...
In this paper we prove that for a restricted affine control system on a connected manifold M, the as...
From a topological point of vien this work deals with the structure of a set of affine and controlla...
We prove the following theorem. Let f be a dominant endomorphism of a projective surface over an alg...
AbstractWe give a topological characterization of ω-limit sets of continuous antitriangular maps, th...
In this thesis, we are studying topological and dynamical conditions imposing infinitely many period...
65 pages. We generalized the results in the first version and add an appendix in collaboration with ...
We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along su...
In this letter we present a decomposition for control systems whose drift vector field is the geod...