37 research outputs found
NMS Flows on S3 with no Heteroclinic Trajectories Connecting Saddle Orbits
In this paper we find topological conditions for the non existence of heteroclinic
trajectories connecting saddle orbits in non singular Morse-Smale flows on S
3
. We obtain
the non singular Morse-Smale flows that can be decomposed as connected sum of flows and
we show that these flows are those who have no heteroclinic trajectories connecting saddle
orbits. Moreover, we characterize these flows in terms of links of periodic orbits
Fundamentos matemáticos de la Ingeniería
Enginyeria Tècnica Agrícola, especialitat d'Hortofructicultura i Jardineria. 803: Fonaments Matemàtics de l'Enginyeri
Dynamics of Newton-like root finding methods
When exploring the literature, it can be observed that the operator obtained when
applying Newton-like root finding algorithms to the quadratic polynomials z2 − c
has the same form regardless of which algorithm has been used. In this paper, we
justify why this expression is obtained. This is done by studying the symmetries of
the operators obtained after applying Newton-like algorithms to a family of degree d
polynomials p(z) = zd −c. Moreover, we provide an iterative procedure to obtain the
expression of new Newton-like algorithms. We also carry out a dynamical study of
the given generic operator and provide general conclusions of this type of methods.Funding for open access charge: CRUE-Universitat Jaume
Bifurcations in the two imaginary centers problem
In this paper we show that, for a given value of the energy, there is a bifurcation
for the two imaginary centers problem. For this value not only the configuration of the orbits
changes but also a change in the topology of the phase space occurs
Bifurcations in the two imaginary centers problem
summary:In this paper we show that, for a given value of the energy, there is a bifurcation for the two imaginary centers problem. For this value not only the configuration of the orbits changes but also a change in the topology of the phase space occurs
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
Altres ajuts: Generalitat Valenciana Project PROMETEO/2016/089 and UJI project P1.1B2015-16We study the Chebyshev-Halley family of root finding algorithms from the point of view of holomorphic dynamics. Numerical experiments show that the speed of convergence to the roots may be slower when the basins of attraction are not simply connected. In this paper we provide a criterion which guarantees the simple connectivity of the basins of attraction of the roots. We use the criterion for the Chebyshev-Halley methods applied to the degree n polynomials zⁿ +c, obtaining a characterization of the parameters for which all Fatou components are simply connected and, therefore, the Julia set is connected. We also study how increasing n affects the dynamics
Dynamics of Newton-like root finding methods
Altres ajuts: project UJI-B2019-18When exploring the literature, it can be observed that the operator obtained when applying Newton-like root finding algorithms to the quadratic polynomials z − c has the same form regardless of which algorithm has been used. In this paper, we justify why this expression is obtained. This is done by studying the symmetries of the operators obtained after applying Newton-like algorithms to a family of degree d polynomials p(z) = z − c. Moreover, we provide an iterative procedure to obtain the expression of new Newton-like algorithms. We also carry out a dynamical study of the given generic operator and provide general conclusions of this type of methods
Convergence regions for the Chebyshev-Halley family
In this paper we study the dynamical behavior of the Chebyshev-Halley methods on the family of degree polynomials . We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having as an attracting fixed point, we show how the basins of attraction of the roots become smaller as the value of grows. We also demonstrate that, although the convergence order of the Chebyshev-Halley family is 3, there is a member of order 4 for each value of . In the case of quadratic polynomials, we bound the set of parameters which correspond to iterative methods with stable behaviour other than the basins of attraction of the roots
Bott Integrable Hamiltonian Systems on S2 x S1
In this paper, we study the topology of Bott integrable Hamiltonian flows on S2 × S1 in terms of some types of periodic orbits, called NMS
periodic orbits. The set of these periodic orbits can be identified by means of
some operations applied on global and local links. These operations come from
the round handle decomposition of these systems on S2 × S1. We apply the
results to obtain a non-integrability criterium.
1. Introduction. Let v = sgrad (H) be a hamiltonia
Newton’s method on Bring-Jerrard polynomials
The first and fourth authors were partially supported by P11B2011-30 (Universitat Jaume I) and by the Spanish grant MTM2011-28636-C02-02. The second and third authors were partially supported by the Catalan grant 2009SGR-792, and by the Spanish grant MTM2011-26995-C02-02. The third author also wants to thank the support of the Polish NCN grant decision DEC-2012/06/M/ST1/00168