3 citations · 6 across the 14 of their papers we have counts for
14 papers
Analytic rigidity and symbolic dynamics for two-centre billiards
Stefano Baranzini, Susanna Terracini
We establish a sharp rigidity--chaos dichotomy for planar two-centre billiards, motivated by a natural analogue of the Birkhoff--Poritsky conjecture: the only tables integrable at…
Scattering Dynamics and Chaotic Motions in a Relativistic Two-Centre Problem
Stefano Baranzini, Gian Marco Canneori
We study the planar relativistic two-centre problem at fixed energy, including a class of perturbations of the Keplerian potential. Up to a reparametrisation of time, the relativis…
Non-integrability of n-centre billiards
Stefano Baranzini
We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall.…
On the Birkhoff conjecture for Kepler billiards
Stefano Baranzini, Vivina L. Barutello, Irene De Blasi +1
We investigate the integrability of Kepler billiards-mechanical billiard systems in which a particle moves under the influence of a Keplerian potential and reflects elastically at…
Frozen planet orbits for the -electron atom
Stefano Baranzini, Gian Marco Canneori, Susanna Terracini
We seek periodic trajectories of a system of multiple mutually repelling electrons on a half-line, with an attractive nucleus sitting at the origin. We adopt a variational viewpoin…
On the Zoll deformations of the Kepler problem
Asselle Luca, Baranzini Stefano
A celebrated result of Bertrand states that the only central force potentials on the plane with the property that all bounded orbits are periodic are the Kepler potential and the p…
Quantitative tightness for three-dimensional contact manifolds: a sub-Riemannian approach
Andrei A. Agrachev, Stefano Baranzini, Eugenio Bellini +1
Through the use of sub-Riemannian metrics we provide quantitative estimates for the maximal tight neighbourhood of a Reeb orbit on a three-dimensional contact manifold. Under appro…
Mountain pass frozen planet orbits in the helium atom model
Stefano Baranzini, Gian Marco Canneori, Susanna Terracini
We seek frozen planet orbits for the helium atom through an application of the Mountain Pass Lemma to the Lagrangian action functional. Our method applies to a wide class of gravit…
Chaotic phenomena for generalised N-centre problems
Stefano Baranzini, Gian Marco Canneori
We study a class of singular dynamical systems which generalise the classical N-centre problem of Celestial Mechanics to the case in which the configuration space is a Riemannian s…
Morse index of circular solutions for attractive central force problems on surfaces
Stefano Baranzini, Alessandro Portaluri, Ran Yang
The classical theory of attractive central force problem on the standard (flat) Euclidean plane can be generalized to surfaces by reformulating the basic underlying physical princi…
Functional determinants for the second variation
Stefano Baranzini
We study the determinant of the second variation of an optimal control problem for general boundary conditions. Generically, this operators are not trace class and the determinant…
Morse index and determinant of block Jacobi matrices via optimal control
Stefano Baranzini, Ivan Beschastnyi
We describe the relation between block Jacobi matrices and minimization problems for discrete time optimal control problems. Using techniques developed for the continuous case, we…
Index theorems for graph-parametrized optimal control problems
Andrei Agrachev, Stefano Baranzini, Ivan Beschastnyi
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications.…
Operators arising as Second Variation of optimal control problems and their spectral asymptotics
Stefano Baranzini
We compute the asymptotic for the eigenvalues of a particular class of compact operators deeply linked with the second variation of optimal control problems. We characterize this f…