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
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.
Moghimi, P. , Asheghi, R. and 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.
MLA
Moghimi, P. , , Asheghi, R. , and Kazemi, R. . "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.
HARVARD
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.
CHICAGO
P. Moghimi , R. Asheghi and R. 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,
VANCOUVER
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.
)
