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Upper bounds on the number of limit cycles in generalized Liénard equations of odd type

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References

  1. M. Caubergh and F. Dumortier, J. Differ. Equations 244, 1359–1394 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  2. F. Dumortier, D. Panazzolo, and R. Roussarie, Proc. Am. Soc. 135, 1895–1904 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Ecalle, Introduction aux fonctions analysables et prevue constructive de la conjecture de Dulac (Hermann, Paris, 1992).

    Google Scholar 

  4. Yu. Ilyashenko, Finitness Theorems for Limit Cycles (Am. Math. Soc., Providence, RI, 1991).

    Google Scholar 

  5. Yu. Ilyashenko, Nonlinearity 13, 1337–1342 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  6. Yu. Ilyashenko and A. Panov, Moscow Math. J. 1, 583–599 (2001).

    MATH  MathSciNet  Google Scholar 

  7. Yu. Ilyashenko and S. Yakovenko, J. Differ. Equations 126, 87–105 (1996).

    Article  MathSciNet  Google Scholar 

  8. A. Lienard, Rev. Gen. Elec., No. 23, 946–954 (1928).

  9. A. Lins Neto, W. de Melo, and C. C. Pugh, Lect. Notes Math. 597, 335–357 (1977).

    Article  Google Scholar 

  10. S. Smale, Math. Intelligencer 20(2), 7–15 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Van der Pol, Philos. Mag. 6(43), 700–719 (1922).

    Google Scholar 

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Correspondence to G. A. Kolyutsky.

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Original Russian Text © G.A. Kolyutsky, 2010, published in Doklady Akademii Nauk, 2010, Vol. 431, No. 1, pp. 12–15.

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Kolyutsky, G.A. Upper bounds on the number of limit cycles in generalized Liénard equations of odd type. Dokl. Math. 81, 176–179 (2010). https://doi.org/10.1134/S106456241002002X

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