An extended complete Chebyshev system of ۳ Abelian integrals related to a non-algebraic Hamiltonian system

In this paper, we study the Chebyshev property of the ۳-dimentional vector space E =\langle I_۰, I_۱, I_۲\rangle, where I_k(h)=\int_{H=h}x^ky\,dx and H(x,y)=\frac{۱}{۲}y^۲+\frac{۱}{۲}(e^{-۲x}+۱)-e^{-x} is a non-algebraic Hamiltonian function. Our main result asserts that E is an extended complete Chebyshev space for h\in(۰,\frac{۱}{۲}). 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.

کلیدواژه ها:

Non-algebraic Hamiltonian ، Abelian integral ، Chebyshev property ، ECT-system