arXiv subjects

Anastasia Sharipova

Publications and source records attributed to Anastasia Sharipova.

2 recordsLinked to original sources

arXiv2019

Viterbo's conjecture for certain Hamiltonians in classical mechanics

We study some particular cases of Viterbo's conjecture relating volumes of convex bodies and actions of closed characteristics on their boundaries, focusing on the case of a Hamiltonian of classical mechanical type, splitting into summands depending on the coordinates and the momentum separately. We manage to establish the conjecture for sublevel sets of convex $2$-homogeneous Hamiltonians of this kind in several particular cases. We also discuss open cases of this conjecture.

math.MG↗

arXiv2015

Elementary approach to closed billiard trajectories in asymmetric normed spaces

We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results.

math.MG↗