We study the Floquet solutions of the Mathieu equation. In order to find an explicit relation between the characteristic exponents and their corresponding eigenvalues of the Mathieu operator, we consider the Whittaker-Hill formula. This gives an explicit relation between the eigenvalue and its characteristic exponent. The equation is explicit up to a determinant of an infinite dimensional matrix. We find a third-order linear recursion for which this determinant is exactly the limit. An explicit solution for third-order linear recursions is obtained which enables us to write the determinant explicitly.Sträng Jan-Eric. On the characteristic exponents of Floquet solutions to the Mathieu equation. In: Bulletin de la Classe des sciences, tome 16...
Summarization: We consider the application of the finite element collocation method, with Hermite cu...
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents....
This paper is concerned with the problem of determining the location of eigenvalues for diagonally d...
AbstractIn this paper we study the infinite linear system MμX=0 equivalent to the Mathieu equation. ...
Abstract. In this paper a method is developed to calculate the Floquet exponents of the matrix-value...
The form of the fundamental set of solutions of the damped Mathieu equation is determined by Floquet...
This thesis consists of two largely independent parts. Part I is a discussion of Campbell's work on ...
The Mathieu equation $X^n$ +(a–2q cos2t)x=0 has been studied in great detail since its discovery in...
AbstractHill's equation is studied for a particular class of periodic functions, which covers a broa...
Consider a second order differential linear periodic equation. The periodic coefficient is an approx...
International audienceWe propose two methods to find analytic periodic approximations intended for d...
We have analyzed the eigenvalues of the Mathieu equation, the Schrodinger\ud equation for the cosine...
It has been shown that a series of three-term recurrence relations of a certain class is a powerful ...
Our objective is to extend the well-known Floquet theory of ordinary differential equations with sin...
We establish an asymptotic lower bound for the minimum excitation needed to cause instability for th...
Summarization: We consider the application of the finite element collocation method, with Hermite cu...
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents....
This paper is concerned with the problem of determining the location of eigenvalues for diagonally d...
AbstractIn this paper we study the infinite linear system MμX=0 equivalent to the Mathieu equation. ...
Abstract. In this paper a method is developed to calculate the Floquet exponents of the matrix-value...
The form of the fundamental set of solutions of the damped Mathieu equation is determined by Floquet...
This thesis consists of two largely independent parts. Part I is a discussion of Campbell's work on ...
The Mathieu equation $X^n$ +(a–2q cos2t)x=0 has been studied in great detail since its discovery in...
AbstractHill's equation is studied for a particular class of periodic functions, which covers a broa...
Consider a second order differential linear periodic equation. The periodic coefficient is an approx...
International audienceWe propose two methods to find analytic periodic approximations intended for d...
We have analyzed the eigenvalues of the Mathieu equation, the Schrodinger\ud equation for the cosine...
It has been shown that a series of three-term recurrence relations of a certain class is a powerful ...
Our objective is to extend the well-known Floquet theory of ordinary differential equations with sin...
We establish an asymptotic lower bound for the minimum excitation needed to cause instability for th...
Summarization: We consider the application of the finite element collocation method, with Hermite cu...
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents....
This paper is concerned with the problem of determining the location of eigenvalues for diagonally d...