68 citations · 90 across the 9 of their papers we have counts for
6 papers · 1 filter
Multiple orthogonal geodesic chords and a proof of Seifert's conjecture on brake orbits
Roberto Giambó, Fabio Giannoni, Paolo Piccione
Using nonsmooth critical point theory, we prove the existence of at least N orthogonal geodesic chords in a class of Riemannian N-disk with strongly concave boundary. This yields a…
On the normal exponential map in singular conformal metrics
R. Giambò, F. Giannoni, P. Piccione
Brake orbits and homoclinics of autonomous dynamical systems correspond, via Maupertuis principle, to geodesics in Riemannian manifolds endowed with a metric which is singular on t…
Morse Theory for geodesics in singular conformal metrics
R. Giambò, F. Giannoni, P. Piccione
Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal facto…
Examples with minimal number of brake orbits and homoclinics in annular potential regions
R. Giambò, F. Giannoni, P. Piccione
We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energ…
Potential wells with a unique brake orbit. Counterexamples to a conjecture by H. Seifert
R. Giambò, F. Giannoni, P. Piccione
In this paper we prove the existence of real-analytic natural Hamiltonian systems - i.e. where H(q,p)=T(q,p)+V(q) in the 2N-dimensional real space, where N is any integer greater t…
Orthogonal Geodesic Chords, Brake Orbits and Homoclinic Orbits in Riemannian Manifolds
Roberto Giambó, Fabio Giannoni, Paolo Piccione
The study of solutions with fixed energy of certain classes of Lagrangian (or Hamiltonian) systems is reduced, via the classical Maupertuis--Jacobi variational principle, to the st…