期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 266, 期 9, 页码 5895-5911出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.10.049
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资金
- National Science Centre of Poland [DEC-2013/09/B/ST1/04130]
- [17H02859]
The autonomous Duffing oscillator, and its van der Pol modification, are known to admit time-dependent first integrals for specific values of parameters. This corresponds to the existence of Darboux polynomials, and in fact more can be shown: that there exist Liouvillian first integrals which do not depend on time. They can be expressed in terms of the Gauss and Kummer hypergeometric functions, and are neither analytic, algebraic nor meromorphic. A criterion for this to happen in a general dynamical system is formulated as well. (C) 2018 Elsevier Inc. All rights reserved.
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