Exploració per tema "Classificació AMS::34 Ordinary differential equations::34A General theory"
Ara es mostren els items 1-20 de 20
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Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
(1997)
Article
Accés obertThe linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain ... -
An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator
(2010)
Article
Accés restringit per política de l'editorialIn this paper, we analytically consider sliding bifurcations of periodic orbits in the dry-friction oscillator. The system depends on two parameters: F, which corresponds to the intensity of the friction, and ω, the ... -
Constraint algorithm for extremals in optimal control problems
(2007-07-27)
Article
Accés obertA characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of ... -
Darboux integrals for Schrödinger planar vector fields via Darboux transformations
(2012-07-14)
Article
Accés obertIn this paper we study the Darboux transformations of planar vector fields of Schr odinger type. Using the isogaloisian property of Darboux transformation we prove the \invariance" of the objects of the \Darboux theory ... -
Effective reducibility of quasiperiodic linear equations close to constant coefficients
(1995)
Article
Accés obertLet us consider the differential equation $$ \dot{x}=(A+\varepsilon Q(t,\varepsilon))x, \;\;\;\; |\varepsilon|\le\varepsilon_0, $$ where $A$ is an elliptic constant matrix and $Q$ depends on time in a quasiperiodic ... -
Estimating distances from quadruples satisfying stability properties to quadruples not satisfying them
(2000)
Article
Accés obertWe consider quadruples of matrices (E,A,B,C) defining generalized linear multivariable time-invariant dynamical systems, with E,A square matrices and B, C rectangular matrices. Using geometrical techniques we present ... -
First derivative of the period function with applications
(2001)
Article
Accés obertGiven a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function. As far as we know, there are no general methods to study ... -
Geometric approach to Pontryagin's Maximum Principle
(Springer Netherlands, 2008-10)
Article
Accés obertSince the second half of the 20th century, Pontryagin’s Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we ... -
Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems
(2009-08-14)
Report de recerca
Accés obertThe geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi ... -
Geometric tools to determine the hyperbolicity of limit cycles
(2005)
Article
Accés obertIn this paper we present a new method to study limit cycles’ hyperbolicity. The main tool is the function ? = ([V,W] ^ V )/(V ^W), where V is the vector field under investigation and W a transversal one. Our approach ... -
Limit cycles and Lie symmetries
(2005)
Article
Accés obertGiven a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem ... -
Morphisms and inverse problems
(2011-11-03)
Report de recerca
Accés obertIn 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 ... -
On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
(2011-01-15)
Article
Accés restringit per política de l'editorialWe 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. ... -
Optimal control problems for affine connection control systems: characterization of extremals
(American Institute of Physics, 2008-02)
Text en actes de congrés
Accés obertPontryagin’s Maximum Principle [8] is considered as an outstanding achievement of optimal control theory. This Principle does not give sufficient conditions to compute an optimal trajectory; it only provides necessary ... -
Psi-series of quadratic vector fields on the plane
(1997)
Article
Accés obertPsi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is ... -
Psi-series, singularities of solutions and integrability of polynomial systems
(1996)
Article
Accés obertPsi-series (i.e., logarithmic series) of $m$-dimensional polynomial systems are considered. Its existence and convergence is studied, and an algorithm of location of logarithmic singularities is developed. Moreover, ... -
Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps
(Elsevier, 2021)
Article
Accés obertIn this paper we study the action of planar birational transformations, also known as plane Cremona maps, on quadratic planar differential systems. We provide geometrical characterizations of when a quadratic system is ... -
Skinner-Rusk unified formalism for optimal control systems and applications
(2007-05-15)
Article
Accés obertA geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed ... -
Strict abnormal extremals in nonholonomic and kinematic control systems
(2008-06)
Article
Accés obertIn optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals ... -
Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a twofold cycle
(2020-01-01)
Article
Accés obertWe study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed ...