5 papers
Canonical separating coordinates in the generalized cubic Hénon-Heiles systems
Alessandro Portaluri, Nicola Sottocornola
We study the three classical integrable generalized cubic Hénon--Heiles systems -- Kaup--Kupershmidt, KdV, and Sawada--Kotera -- from the viewpoint of bi-Hamiltonian geometry…
Index theory for non-compact quantum graphs
Daniele Garrisi, Alessandro Portaluri, Li Wu
We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov…
Non-minimality and instability of brake orbits for natural Lagrangians on Riemannian manifolds
Luca Asselle, Xijun Hu, Alessandro Portaluri +1
We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit…
Morse index theorem for heteroclinic, homoclinic and halfclinic orbits of Lagrangian systems
Xijun Hu, Alessandro Portaluri, Li Wu +1
The purpose of this paper is to prove a new, more general version of the Morse index theorem for heteroclinic, homoclinic, and half-clinic solutions in general Lagrangian systems.…
Index theory for singular Lagrangian systems and Bessel-type differential operators
Xijun Hu, Alessandro Portaluri, Li Wu
The aim of the present manuscript is to develop an index theory for singular Lagrangian systems, with a particular focus on the important class of singular operators given by Besse…