Zobrazeno 1 - 10
of 520
pro vyhledávání: '"Giannoni, F."'
We study the non-autonomous variational problem: \begin{equation*} \inf_{(\phi,\theta)} \bigg\{\int_0^1 \bigg(\frac{k}{2}\phi'^2 + \frac{(\phi-\theta)^2}{2}-V(x,\theta)\bigg)\text{d}x\bigg\} \end{equation*} where $k>0$, $V$ is a bounded continuous fu
Externí odkaz:
http://arxiv.org/abs/2204.07455
Using an estimate on the number of critical points for a Morse-even function on the sphere $\mathbb S^m$, $m\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean
Externí odkaz:
http://arxiv.org/abs/1503.06176
Let $(M,g)$ be a (complete) Riemannian surface, and let $\Omega\subset M$ be an open subset whose closure is homeomorphic to a disk. We prove that if $\partial\Omega$ is smooth and it satisfies a strong concavity assumption, then there are at least t
Externí odkaz:
http://arxiv.org/abs/1503.05805
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 the boundary (Jacobi metric). Motivated by the classical, yet still int
Externí odkaz:
http://arxiv.org/abs/1503.05804
Publikováno v:
J. Differential Equations 256 (2014) 2677-2690
We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value
Externí odkaz:
http://arxiv.org/abs/1406.0642
Publikováno v:
Communications in Analysis and Geometry, Volume 22, Issue 5, 2014, Pages 779-809
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 factors vanishing on a regular hypersurface of a Riemannian manifold.
Externí odkaz:
http://arxiv.org/abs/1406.0644
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 than 1 - with non critical energy levels E for the potential V such tha
Externí odkaz:
http://arxiv.org/abs/1203.5198
Publikováno v:
Nonlinear Analysis, Theory, Methods and Applications Volume 73, Issue 2, 15 July 2010, Pages 290-337
In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link of the multiplicity problem with the famous S
Externí odkaz:
http://arxiv.org/abs/1003.3846
Publikováno v:
J.Math.Phys.49:042504,2008
The gravitational collapse of a wide class of self-interacting homogeneous scalar fields models is analyzed. The class is characterized by certain general conditions on the scalar field potential, which, in particular, include both asymptotically pol
Externí odkaz:
http://arxiv.org/abs/0802.0992
The general relativistic dynamics of a wide class of self-interacting, self-gravitating homogeneous scalar fields models is analyzed. The class is characterized by certain general conditions on the scalar field potential, which include both asymptoti
Externí odkaz:
http://arxiv.org/abs/math/0703512