Zobrazeno 1 - 10
of 181
pro vyhledávání: '"Portaluri, Alessandro"'
The classical theory of attractive central force problem on the standard (flat) Euclidean plane can be generalized to surfaces by reformulating the basic underlying physical principles by means of differential geometry. Attractive central force probl
Externí odkaz:
http://arxiv.org/abs/2305.18134
Morse index theory provides an elegant and useful tool for describing several aspects of a Lagrangian system in terms of its variational properties. In the classical framework it provides an equality between the spectral properties of a second order
Externí odkaz:
http://arxiv.org/abs/2301.06900
In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe degenerat
Externí odkaz:
http://arxiv.org/abs/2109.12022
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 September 2024 537(1)
For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, $d\ge 2$, the simplest possible periodic solutions are provided by circular relative equilibria, (RE) for short, namely solutions in which each body rigidly ro
Externí odkaz:
http://arxiv.org/abs/2105.15009
For the gravitational $n$-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration featuring suitabl
Externí odkaz:
http://arxiv.org/abs/2011.09291
Autor:
Asselle, Luca, Portaluri, Alessandro
For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, the simplest possible solutions are provided by those rigid motions (homographic solutions) in which each body moves along a Keplerian orbit and the configurat
Externí odkaz:
http://arxiv.org/abs/2009.10118
Autor:
Portaluri, Alessandro, Wu, Li
In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This invariant was de
Externí odkaz:
http://arxiv.org/abs/2006.00956
Classical Sturm non-oscillation and comparison theorems as well as the Sturm theorem on zeros for solutions of second order differential equations have a natural symplectic version, since they describe the rotation of a line in the phase plane of the
Externí odkaz:
http://arxiv.org/abs/2005.08034
The aim of this paper is to prove a new and general version of the Morse index theorem for heteroclinic, homoclinic and halfclinic solutions of general Lagrangian systems. In the last section we compute the Morse index of some heteroclinic and halfcl
Externí odkaz:
http://arxiv.org/abs/2004.08643