26 citations · 74 across the 18 of their papers we have counts for
21 papers
Non Quasi-Periodic Normal Form Theory
Gabriella Pinzari
We review a recent generalization of Normal Form Theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main…
Quantitative KAM theory, with an application to the three-body problem
Gabriella Pinzari, Xiang Liu
Based on quantitative ``{\sc kam} theory'', we state and prove two theorems about the continuation of maximal and whiskered quasi--periodic motions to slightly perturbed systems ex…
Perturbation theory and canonical coordinates in celestial mechanics
Gabriella Pinzari
KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by V.I.Arnold in the 60s who…
A new analysis of the three--body problem
Jerome Daquin, Sara Di Ruzza, Gabriella Pinzari
In the recent papers~[18],~[5], respectively, the existence of motions where the perihelions afford periodic oscillations about certain equilibria and the onset of a topological ho…
Proof of a conjecture by H. Dullin and R. Montgomery
Gabriella Pinzari
In the framework of the planar Euler problem in the quasi--periodic regime, the formulae of the periods available in the literature are simple only on one side of their singularity…
Euler integral as a source of chaos in the three-body problem
Sara Di Ruzza, Gabriella Pinzari
In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "…
Exponential stability of fast driven systems, with an application to celestial mechanics
Qinbo Chen, Gabriella Pinzari
We construct a normal form suited to {\it fast driven systems}. We call so systems including actions , angles {}, and one fast coordinate , moving under the action o…
Symbolic dynamics in a binary asteroid system
Sara Di Ruzza, Jérôme Daquin, Gabriella Pinzari
We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned…
Lonely planets and light belts: the Statistical Mechanics of Gravitational Systems
Gabriella Pinzari, Benedetto Scoppola, Alessio Troiani
In this paper we propose a notion of stability, that we call -stability, for systems of particles interacting via Newton's gravitational potential, and orbiting a much bigger…
Euler integral and perihelion librations
Gabriella Pinzari
We discuss dynamical aspects of an analysis of the two--centre problem started in [15]. The perturbative nature of our approach allows us to foresee applications to the three--body…
Perihelion librations in the secular three--body problem
Gabriella Pinzari
A normal form theory for non--quasi--periodic systems is combined with the special properties of the partially averaged Newtonian potential pointed out in [15] to prove, in the ave…
Exponential stability of Euler integral in the three--body problem
Gabriella Pinzari
The first integral characteristic of the two--centres problem is proven to be an approximate integral (in the sense of N.N.Nekhorossev) to the three--body problem, at least if the…
A Normal Form without small divisors
Gabriella Pinzari
Following the techniques of [4], we formulate a Normal Form Lemma suited to close to be integrable Hamiltonian systems where not all the coordinates are action angles. The Lemma tu…
An analysis of the Sun-Earth-Asteroid systems based on the two-centre problem
Gabriella Pinzari
We propose a new analysis of the two--centre problem particularly suited to be used as a basis to study the dynamics of Sun--Earth--Asteroid systems. Our method, based on a tricky…
On the co--existence of maximal and whiskered tori for the planetary three--body problem
Gabriella Pinzari
In this paper we discuss about the possibility of {\it coexistence} of stable and unstable quasi--periodic {\sc kam} tori in a region of phase space of the three-body problem. The…
A first integral to the partially averaged Newtonian potential of the three-body problem
Gabriella Pinzari
We consider the partial average i.e., the Lagrange average with respect to {\it just one} of the two mean anomalies, of the Newtonian part of the perturbing function in the three--…
Perihelia reduction and global Kolmogorov tori in the planetary problem
Gabriella Pinzari
We prove the existence of an almost full measure set of --dimensional quasi periodic motions in the planetary problem with masses, with eccentricities arbitrarily c…
Canonical coordinates for the planetary problem
Gabriella Pinzari
In 1963, V. I. Arnold stated his celebrated Thorem on the Stability of Planetary Motions. The general proof of his wonderful statement (that he provided completely only for the par…
Global Kolmogorov tori in the planetary N-body problem. Announcement of result
Gabriella Pinzari
We improve a result in [L. Chierchia and G. Pinzari, Invent. Math. 2011] by proving the existence of a positive measure set of --dimensional quasi--periodic motions in the…
Aspects of the planetary Birkhoff normal form
Gabriella Pinzari
The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem…
On the Kolmogorov set for Many-Body Problems
Gabriella Pinzari
I defended my PhD Thesis in Rome, Università Roma Tre, on April, 23, 2009, under the direction of Professor Luigi Chierchia. The judging committee was composed by Professors M. Ber…