Seeking Darboux Polynomials
نویسندگان
چکیده
منابع مشابه
Seeking Darboux polynomials
We introduce several techniques which allow to simplify the expression of the cofactor of Darboux polynomials of polynomial differential systems in Rn. We apply these techniques to some well-known systems when n = 2, 3, 4. We also propose a general method for computing Darboux polynomials in the plane. As an application we prove that a family of potential systems, that includes the van der Pol ...
متن کاملDarboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems
We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function. Moreover, we show that, in a case when the degree of potential is odd, the system does not admit any proper Darboux polynomial, i.e., the ...
متن کاملOn the Christoffel–darboux Formula for Generalized Matrix Orthogonal Polynomials
We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials.
متن کامل7R Darboux Linkages by Factorization of Motion Polynomials
In this paper, we construct two types of 7R closed single loop linkages by combining different factorizations of a general (non-vertical) Darboux motion. These factorizations are obtained by extensions of a factorization algorithm for a generic rational motion. The first type of 7R linkages has several one-dimensional configuration components and one of them corresponds to the Darboux motion. T...
متن کاملTwo-step Darboux Transformations and Exceptional Laguerre Polynomials
It has been recently discovered that exceptional families of SturmLiouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Laguerre and Jacobi. In this paper we show how new families of exceptional orthogonal polynomials can be constructed by means of multiple-step algebraic Darboux transformations. The construction is illustrated with an examp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2014
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-014-9974-0