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Second Order Melnikov Functions of Piecewise Hamiltonian Systems Jean-Pierre Françoise 2159c0f3771eed8a0a654cf59fb44ad8 upmc.fr jean-pierre-francoise 10607 32164-10607 https://orcid.org/0000-0003-0699-1450 https://www.idref.fr/076182193 Jiang Yu 1611032-0 Peixing Yang d8ab49f32278d03f743ba0f2d1899fe0 sjtu.edu.cn 1066273 1806344-1066273 Gestionnaire HAL 5 Sorbonne Université 7cfd4753d4999726e403d99c5b54331a sorbonne-universite.fr 2020-03-13 10:55:31 2024-10-30 13:34:18 2020-03-13 13:18:10 2020-01 2020-03-13 contributor Gestionnaire HAL 5 Sorbonne Université 7cfd4753d4999726e403d99c5b54331a sorbonne-universite.fr CCSD hal-02507452 https://hal.sorbonne-universite.fr/hal-02507452 francoise:hal-02507452 <i>International journal of bifurcation and chaos in applied sciences and engineering </i>, 2020, 12 (01), pp.29 - 31. <a target="_blank" href="https://dx.doi.org/10.1142/S0218127420500169">⟨10.1142/S0218127420500169⟩</a> International journal of bifurcation and chaos in applied sciences and engineering , 2020, 12 (01), pp.29 - 31. ⟨10.1142/S0218127420500169⟩ HAL Authorization CNRS - Centre national de la recherche scientifique CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions Laboratoire Jacques-Louis Lions Sorbonne Université Sorbonne Université 01/01/2018 Faculté des Sciences de Sorbonne Université Université Paris Cité Université Paris Cité Université Paris Cité - Faculté des Sciences Sorbonne Université - Texte Intégral Alliance Sorbonne Université Mathématiques + Informatique International No Yes Second Order Melnikov Functions of Piecewise Hamiltonian Systems Jean-Pierre Françoise 2159c0f3771eed8a0a654cf59fb44ad8 upmc.fr jean-pierre-francoise 10607 32164-10607 https://orcid.org/0000-0003-0699-1450 https://www.idref.fr/076182193 Jiang Yu 1611032-0 Peixing Yang d8ab49f32278d03f743ba0f2d1899fe0 sjtu.edu.cn 1066273 1806344-1066273 14353 0218-1274 1793-6551 International journal of bifurcation and chaos in applied sciences and engineering World Scientific Publishing 12 01 29 - 31 2020-01 10.1142/S0218127420500169 English Limit cycles Bifurcation Piecewise Hamiltonian system Melnikov functions Mathematics [math] Journal articles Journal articles Journal articles

In this paper, we consider the general perturbations of piecewise Hamiltonian systems. A formula for the second order Melnikov functions is derived when the first order Melnikov functions vanish. As an application, we can improve an upper bound of the number of bifurcated limit cycles of a piecewise Hamiltonian system with quadratic polynomial perturbations.

099222221 199712644L Laboratoire Jacques-Louis Lions LJLL (UMR_7598) 2019-12-31

Sorbonne-Université, Boîte courrier 187 - 75252 Paris Cedex 05

https://www.ljll.math.upmc.fr School of Mathematical Sciences [Shanghai]

Fudan University220 Handan RoadShanghai 200433

http://math.fudan.edu.cn/en/ School of Mathematical Sciences [Shanghai]

Tongji Univ, School of Mathematical Sciences, Shanghai 200092, Peoples R China

http://math.tongji.edu.cn/en/Default.aspx 027542084 0000000121514068 https://ror.org/02n7qrg46 Université Paris Diderot - Paris 7 UPD7 2019-12-31

5 rue Thomas-Mann - 75205 Paris cedex 13

http://www.univ-paris-diderot.fr 221333754 https://ror.org/02en5vm52 Sorbonne Université SU 2018-01-01

21 rue de l’École de médecine - 75006 Paris

http://www.sorbonne-universite.fr/ 02636817X 0000000122597504 https://ror.org/02feahw73 Centre National de la Recherche Scientifique CNRS 1939-10-19

https://www.cnrs.fr/ https://ror.org/013q1eq08 Fudan University [Shanghai]

Shanghai, Yangpu

http://www.fudan.edu.cn/englishnew/ https://ror.org/03rc6as71 Tongji University

1239 Siping Road, Shanghai

https://en.tongji.edu.cn/