University of TabrizComputational Methods for Differential Equations2345-39826420181001An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system4384477715ENPegah MoghimiDepartment of Mathematical Sciences,
Isfahan University of Technology,
Isfahan, Iran, 84156-83111Rasoul AsheghiDepartment of Mathematical Sciences,
Isfahan University of Technology,
Isfahan, Iran, 84156-83111Rasool KazemiDepartment of Mathematical Sciences,
University of Kashan, Kashan, Iran, 87317-53153Journal Article20171209In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, 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 $hin(0,frac{1}{2})$. 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.http://cmde.tabrizu.ac.ir/article_7715_658154616797cb8e27927c86cb9b9d39.pdf