Moghimi, P., Asheghi, R., Kazemi, R. (2018). An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system. Computational Methods for Differential Equations, 6(4), 438-447.

Pegah Moghimi; Rasoul Asheghi; Rasool Kazemi. "An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system". Computational Methods for Differential Equations, 6, 4, 2018, 438-447.

Moghimi, P., Asheghi, R., Kazemi, R. (2018). 'An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system', Computational Methods for Differential Equations, 6(4), pp. 438-447.

Moghimi, P., Asheghi, R., Kazemi, R. An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system. Computational Methods for Differential Equations, 2018; 6(4): 438-447.

An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system

^{1}Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111

^{2}Department of Mathematical Sciences, University of Kashan, Kashan, Iran, 87317-53153

Receive Date: 09 December 2017,
Accept Date: 25 August 2018

Abstract

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =\langle I_0, I_1, I_2\rangle$, where $I_k(h)=\int_{H=h}x^ky\,dx$ and $H(x,y)=\frac{1}{2}y^2+\frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $h\in(0,\frac{1}{2})$. To this end, we use the criterion and tools developed by Grau et al. in \cite{Grau} to investigate when a collection of Abelian integrals is Chebyshev.