A Chebyshev criterion with applications
Armengol Gasull, Anna Geyer, Francesc Mañosas
Abstract
We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic non-autonomous ODEs to determine bounds on the number of isolated periodic solutions, as well as to persistence problems of periodic solutions for perturbed Hamiltonian systems.
Topics & Concepts
MathematicsChebyshev filterOdeChebyshev polynomialsChebyshev equationApplied mathematicsHamiltonian systemContext (archaeology)Mathematical analysisChebyshev iterationPure mathematicsClassical orthogonal polynomialsOrthogonal polynomialsPaleontologyBiologyAdvanced Differential Equations and Dynamical SystemsQuantum chaos and dynamical systemsLipid metabolism and biosynthesis