Towards the proof of Yoshida's conjecture
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F15%3A%230000501" target="_blank" >RIV/47813059:19610/15:#0000501 - isvavai.cz</a>
Result on the web
<a href="http://iopscience.iop.org/article/10.1088/0951-7715/28/9/3389/meta" target="_blank" >http://iopscience.iop.org/article/10.1088/0951-7715/28/9/3389/meta</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/0951-7715/28/9/3389" target="_blank" >10.1088/0951-7715/28/9/3389</a>
Alternative languages
Result language
angličtina
Original language name
Towards the proof of Yoshida's conjecture
Original language description
Yoshida's conjecture formulated by Yoshida in 1989 states that in C-2N equipped with the canonical symplectic form dp boolean AND dq, the Hamiltonian flow corresponding to the Hamiltonian H = 1/2 Sigma(N)(i=1) p(i)(2) + Sigma(N)(i=0) (q(i) - q(i+1))(k),with q(0) = q(N+1) = 0, where N >= 3 is odd and k >= 4 is even, has no global complex meromorphic first integral functionally independent of H. For N = 3 and N = 5 with k >= 4 arbitrary even number, the result was proved true by Maciejewski (2012 Nonlinearity 25 255-77) by means of differential Galois theory. However, the question as to 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 Costin, which are based on the so-called poly-Painleve method devised by Kruskal.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/EE2.3.20.0002" target="_blank" >EE2.3.20.0002: Development of Research Capacities of the Mathematical Institute in Opava</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinearity
ISSN
0951-7715
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
9
Country of publishing house
GB - UNITED KINGDOM
Number of pages
13
Pages from-to
3389-3401
UT code for WoS article
000360499900015
EID of the result in the Scopus database
2-s2.0-84940093620