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- W3100774162 abstract "Yoshida's Conjecture formulated by H. Yoshida in 1989 states that in $mathbb{C}^{2N}$ equipped with the canonical symplectic form $mathrm{d}mathbf{p} wedge mathrm{d} mathbf{q},$ the Hamiltonian flow corresponding to the Hamiltonian function begin{equation*} H = frac{1}{2}sum_{i=1}^{N} p_{i}^{2} sum_{i=1}^{N} p_{i}^{2} + sum_{i=0}^{N} (q_i - q_{i+1})^k, quad text{with } q_0 = q_{N+1} = 0, label{system} end{equation*} where $Ngeq 3$ is odd and $kgeq 4$ is even, has no meromorphic first integral functionally independent of $H$. For $N=3$ and $N=5$ with $kgeq 4$ arbitrary even number, the result was proved true by Maciejewski, Przybylska and Yoshida in 2012 by means of differential Galois theory. However, the question whether Yoshida's conjecture is true in general, remained open. In this paper we give a proof that this conjecture is in fact true for infinitely many values of $N$ using the results of R. D. Costin which are based on the so-called poly-Painlev'{e} method devised by M. Kruskal." @default.
- W3100774162 created "2020-11-23" @default.
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- W3100774162 date "2015-08-20" @default.
- W3100774162 modified "2023-09-25" @default.
- W3100774162 title "Towards the proof of Yoshida’s conjecture" @default.
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- W3100774162 doi "https://doi.org/10.1088/0951-7715/28/9/3389" @default.
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