Photo by arindam_mahanta from unsplash
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… Click to show full abstract
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.
Keywords:
mechanics;
hamiltonians classical;
certain hamiltonians;
conjecture;
conjecture certain;
viterbo conjecture
Journal Title: Arnold Mathematical Journal
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Arnold Mathematical Journal
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!