45 citations · 133 across the 45 of their papers we have counts for
52 papers
Morse Index, Stability and Spectral Bounds for Periodic Orbits in Reversible Lagrangian Systems
Alessandro Portaluri, Li Wu
We prove quantitative stability and instability estimates for reversible periodic solutions of strictly Legendre-convex Lagrangian systems. If the configuration dimension is , t…
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 a…
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…
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…
Morse Index for Homothetic motions in the gravitational n-body problem
Yuwei Ou, Alessandro Portaluri
In the gravitation n-body Problem, a homothetic orbit is a special solution of the Newton's Equations of motion, in which each body moves along a straight line through the center o…
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…