TY - JOUR
ID - 7715
TI - An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Moghimi, Pegah
AU - Asheghi, Rasoul
AU - Kazemi, Rasool
AD - Department of Mathematical Sciences,
Isfahan University of Technology,
Isfahan, Iran, 84156-83111
AD - Department of Mathematical Sciences,
University of Kashan, Kashan, Iran, 87317-53153
Y1 - 2018
PY - 2018
VL - 6
IS - 4
SP - 438
EP - 447
KW - Non-algebraic Hamiltonian
KW - Abelian integral
KW - Chebyshev property
KW - ECT-system
DO -
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_7715.html
L1 - https://cmde.tabrizu.ac.ir/article_7715_658154616797cb8e27927c86cb9b9d39.pdf
ER -