Vivina Barutello
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Vivina Barutello has a total of 1 co-authors. Here are the top co-authors by number of shared publications:
- Susanna Terracini
Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Torino, Italy
2 shared publications
Latest Publications
- Open Access
A bisection algorithm for the numerical Mountain Pass
We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high dimensions, consists in the low number of flow lines to be computed for its convergence; for this reason it improves the one currently used and proposed by Y.S. Choi and P.J. McKenna.
Open AccessA bisection algorithm for the numerical Mountain Pass
We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high dimensions, consists in the low number of flow lines to be computed for its convergence; for this reason it improves the one currently used and proposed by Y.S. Choi and P.J. McKenna.
- Open Access
Action minimizing orbits in the n-body problem with simple choreography constraint
In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in $\RR^d$ under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of $x \in H^1_{2 \pi}(\RR,\RR^d)$ such that $q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, $ where $\tau = 2\pi / n$. In this setting, we first prove that for every $d,n \in \NN$ and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Open AccessAction minimizing orbits in the n-body problem with simple choreography constraint
In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in $\RR^d$ under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of $x \in H^1_{2 \pi}(\RR,\RR^d)$ such that $q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, $ where $\tau = 2\pi / n$. In this setting, we first prove that for every $d,n \in \NN$ and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.