On coexistence of homoclinic and periodic trajectories
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 207-217.

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The coexistence of different types of homoclinic and periodic trajectories for dynamical systems generated by continuous maps of interval into itself is investigated.
Keywords: homoclinic trajectory, type of periodic trajectory, cycle
Mots-clés : cyclic permutation.
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V. V. Fedorenko; A. N. Sharkovsky. On coexistence of homoclinic and periodic trajectories. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 207-217. http://geodesic.mathdoc.fr/item/ND_2010_6_1_a14/

[1] S. V. Gonchenko, L. P. Shilnikov (eds.), Gomoklinicheskie kasaniya, Sb. st., NITs “Regulyarnaya i khaoticheskaya dinamika”, Inst. kompyuter. issled., M.-Izhevsk, 2007, 524 pp.

[2] Sharkovskii A. N., “Sosuschestvovanie tsiklov nepreryvnogo preobrazovaniya pryamoi v sebya”, Ukr. matem. zhurn., 16:1 (1964), 61–71

[3] Sharkovskii A. N., “O probleme izomorfizma dinamicheskikh sistem”, Tr. V Mezhdunar. konf. po nelineinym kolebaniyam, v. 2, Naukova dumka, Kiev, 1970, 541–545

[4] Block L., “Homoclinic points of mappings of the interval”, Proc. Amer. Math. Soc., 72:3 (1978), 576–580 | DOI | MR | Zbl

[5] Fedorenko V. V., Sharkovskii A. N., “Ustoichivost svoistva dinamicheskoi sistemy imet gomoklinicheskuyu traektoriyu”, Ostsillyatsiya i ustoichivost reshenii differentsialno-funktsionalnykh uravnenii, Sb. st., Inst. matematiki AN USSR, Kiev, 1982, 111–113 | MR

[6] Fedorenko V. V., Sharkovskii A. N., “O sosuschestvovanii periodicheskikh i gomoklinicheskikh traektorii”, Vsesoyuzn. konf. po kachestvennoi teorii differentsialnykh uravnenii, Tez. dokl., Shtiintsa, Kishinev, 1979, 174–175

[7] Sharkovskii A. N., Kolyada S. F., Sivak A. G., Fedorenko V. V., Dinamika odnomernykh otobrazhenii, Naukova dumka, Kiev, 1989, 216 pp. | MR

[8] Sharkovskii A. N., “Ob odnoi klassifikatsii nepodvizhnykh tochek”, Ukr. matem. zhurn., 17:5 (1965), 80–95 | MR

[9] Blokh A. M., “Ob odnoi interpretatsii teoremy A. N. Sharkovskogo”, Ostsillyatsiya i ustoichivost reshenii differentsialno-funktsionalnykh uravnenii, Sb. st., Inst. matematiki AN USSR, Kiev, 1982, 3–8 | MR