Now showing items 1-20 of 24

• #### A new approach to the vakonomic mechanics ﻿

(2014-11-01)
Article
Restricted access - publisher's policy
The aim of this paper was to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider ...
• #### Analytic integrability of Bianchi Class A cosmological models with k=1 ﻿

(2012)
Article
Restricted access - publisher's policy
We complete the study of the analytic integrability of the Class A of Bianchi cosmological models with k=1, characterizing the analytic first integrals of the Bianchi types V I0 and V III0.
• #### Axiomatic definition of the topological entropy on the interval ﻿

(2000)
Article
Open Access
Summary. The aim of this paper is to give an axiomatic definition of the topological entropy for continuous interval maps and, in such a way, to shed some more light on the importance of the different properties of the ...
• #### Bifurcation of relative equilibria of the (1+3)-body problem ﻿

(2015-04-02)
Article
Open Access
We study the relative equilibria of the limit case of the planar Newtonian 4-body problem when three masses tend to zero, the so-called (1+3)-body problem. Depending on the values of the infinitesimal masses the number of ...
• #### Centers and uniform isochronous centers of planar polynomial differential systems ﻿

(2018-09)
Article
Open Access
For planar polynomial vector fields of the form (-y+X(x,y))¿¿x+(x+Y(x,y))¿¿y, where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which ...
• #### Centers of quasi-homogeneous polynomial differential equations of degree three ﻿

(2014-03-20)
Article
Restricted access - publisher's policy
We characterize the centers of the quasi-homogeneous planar polynomial differential systems of degree three. Such systems do not admit isochronous centers. At most one limit cycle can bifurcate from the periodic orbits of ...
• #### Central configurations of the planar coorbial satellite problem ﻿

(2004-10)
Article
Open Access
We study the planar central configurations of the 1 +n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2=n=4. Numerically, ...
• #### Central configurations of the planar coorbital satellite problem ﻿

(2003)
Article
Open Access
We study the planar central conﬁgurations of the 1 + n body problem where one mass is large and the other n masses are inﬁnitesimal and equal. We ﬁnd analytically all these central conﬁgurations when 2 ≤ n ≤ 4. Numerically, ...
• #### Counterexample to a conjecture on the algebraic limit cycles of polynomial vector fields ﻿

(2004)
Article
Open Access
In Geometriae Dedicata 79 (2000), 101{108, Rudolf Winkel conjectured: For a given algebraic curve f = 0 of degree m > 4 there is in general no polynomial vector ¯eld of degree less than 2m ¡ 1 leaving invariant f = 0 ...
• #### Darboux integrability and invariant algebraic curves for planar polynomial systems ﻿

(2004)
Article
Open Access
In this paper we study the normal forms of polynomial systems having a set of given generic invariant algebraic curves.
• #### Darboux theory of integrability for a class of nonautonomous vector fields ﻿

(2009-10)
Article
Open Access
The goal of this paper is to extend the classical Darboux theory of integrability from autonomous polynomial vector fields to a class of nonautonomous vector fields. We also provide sufficient conditions for applying ...
• #### Horseshoe periodic orbits for saturn coorbital satellites ﻿

(2000)
Article
Open Access
We consider the motion of coorbital satellites in the framework of the Restricted Three-Body problem for u=6.5*10^(-9). We show a mechanism to generate horsehoe periodic orbits and we compute some families of horseshoe ...
• #### Horseshoe periodic orbits in the restricted three body problem ﻿

(2001)
Article
Open Access
• #### Limit cycles bifurcating from a degenerate center ﻿

(2016-02-01)
Article
Open Access
We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of ...
• #### Morphisms and inverse problems ﻿

(2011-11-03)
External research report
Open Access
In order to investigate polynomial vector ¯elds admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the a±ne plane. In particular, such morphisms may be used to remove ...
• #### Morphisms and inverse problems for Darboux integrating factors ﻿

(2013-12)
Article
Open Access
Polynomial vector fields which admit a prescribed Darboux integrat- ing factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane ...
• #### On the 16th Hilbert problem for algebraic limit cycles ﻿

(2010-03-15)
Article
Restricted access - publisher's policy
For a polynomial planar vector field of degree n ≥ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + (n − 1)(n − 2)/2 when n is even, and (n − 1)(n − 2)/2 when n is ...
• #### On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves ﻿

(2011-01-15)
Article
Restricted access - publisher's policy
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. ...
• #### On the central configurations of the planar 1 + 3 body problem ﻿

(2011)
Article
Open Access
We consider the Newtonian 4 body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two diferent classes of central ...
• #### Periodic orbits of horseshoe type in the planar restricted three-body problem ﻿

(2002)
Article
Open Access