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Title: Šarkovského věta a diferenciální rovnice (Czech)
Title: Sharkovkii theorem and differential equations (English)
Author: Andres, Jan
Language: Czech
Journal: Pokroky matematiky, fyziky a astronomie
ISSN: 0032-2423
Volume: 49
Issue: 2
Year: 2004
Pages: 151-159
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Category: math
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Keyword: Sharkovkii theorem
Keyword: first order nonlinear differential equations
MSC: 34C25
MSC: 37C10
MSC: 37E15
MSC: 39A99
MSC: 58F20
idZBL: Zbl 1265.37016
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Date available: 2010-12-11T20:28:38Z
Last updated: 2015-11-29
Stable URL: http://hdl.handle.net/10338.dmlcz/141221
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Related article: http://dml.cz/handle/10338.dmlcz/147803
Related article: http://dml.cz/handle/10338.dmlcz/141710
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Reference: [A1] Andres, J.: Nielsen number, Artin braids, Poincaré operators and multiple nonlinear oscillations.Nonlin. Anal. 47, 2 (2001), 1017–1028. Zbl 1042.37506, MR 1970714, 10.1016/S0362-546X(01)00242-5
Reference: [A2] Andres, J.: Period three implications for expansive maps in ${\mathbb {R}}^n$.J. Difference Eqns 10, 1 (2004), 17–28. MR 2033331, 10.1080/1023619031000114314
Reference: [AFJ] Andres, J., Fišer, J., Jüttner, L.: On a multivalued version of the Sharkovskii theorem and its application to differential inclusions.Set-Valued Anal. 10, 1 (2002), 1–14. Zbl 1082.37048, MR 1888453, 10.1023/A:1014488216807
Reference: [AG] Andres, J., Górniewicz, L.: Topological Fixed Point Principles for Boundary Value Problems.Kluwer, Dordrecht 2003. Zbl 1029.55002, MR 1998968
Reference: [AJ] Andres, J., Jüttner, L.: Period three plays a negative role in a multivalued version of Sharkovskii’s theorem.Nonlin. Anal. 51 (2002), 1101–1104. Zbl 1015.37032, MR 1926088, 10.1016/S0362-546X(01)00876-8
Reference: [AJP] Andres, J., Jüttner, L., Pastor, K.: On a multivalued version of the Sharkovskii theorem and its application to differential inclusions II.Set-Valued Anal. (v tisku). MR 2128697
Reference: [AP1] Andres, J., Pastor, K.: On a multivalued version of the Sharkovskii theorem and its application to differential inclusions III.Topol. Meth. Nonlin. Anal. 22 (2003), 369–386. Zbl 1059.47057, MR 2036383
Reference: [AP2] Andres, J., Pastor, K.: A version of Sharkovskii’s theorem for differential equations.Proc. Amer. Math. Soc. (v tisku). Zbl 1063.34030, MR 2093067
Reference: [B] Boyland, P.: An analog of Sharkovski’s theorem for twist maps.Contemp. Math., vol. 81, Amer. Math. Soc., Providence, R. I., 1988, 119–133. Zbl 0677.58039, MR 0986261, 10.1090/conm/081/986261
Reference: [BB] Barton, R., Burns, K.: A simple special case of Sharkovskii’s theorem.Amer. Math. Monthly 107, 10 (2000), 932–933. Zbl 0979.37016, MR 1807003
Reference: [BK] Bobok, J., Kuchta, M.: X-minimal patterns and generalization of Sharkovskii’s theorem.Fund. Math. 156 (1998), 33–66. MR 1610555
Reference: [F] Filippov, A. F.: Differenciaľnyje uravnenija s razryvnoj pravoj častju.Nauka, Moskva, 1985.
Reference: [G] Gleick, J.: Chaos.Ando Publ., Praha 1996.
Reference: [H] Handel, M.: The forcing partial order on three times punctured disk.Ergod. Th. Dynam. Sys. 17 (1997), 593–610. MR 1452182, 10.1017/S0143385797084940
Reference: [Ka] Kampen, J.: On fixed points of maps and iterated maps and applications.Nonlin. Anal. 42 (2000), 509–532. Zbl 0967.37014, MR 1775390, 10.1016/S0362-546X(99)00111-X
Reference: [KH] Katok, A., Hasselblatt, B.: Introduction to the Modern Theory Dynamical Systems.Cambridge Univ. Press, Cambridge 1995. MR 1326374
Reference: [Kl] Kloeden, P. E.: On Sharkovsky’s cycle coexisting ordering.Bull. Austral. Math. Soc. 20 (1979), 171–177. MR 0557223, 10.1017/S0004972700010819
Reference: [Kr] Krasnoseľskij, M. A.: Operator sdviga po trajektoriam differenciaľnych uravnenij.Nauka, Moskva 1966.
Reference: [KSS] Kannan, V., Saradhi, P. V. S. P., Seshasai, S. P.: A generalization of Sharkovskii theorem to higher dimensions.J. Nat. Acad. Math. India (Special volume to dedicate Prof. Dr. R. S. Mishra on the occasion of his 80th birthday), 11 (1995), 69–82.
Reference: [LY] Li, T.-Y., Yorke, J.: Period three implies chaos.Amer. Math. Monthly 82 (1975), 985–992. Zbl 0351.92021, MR 0385028, 10.2307/2318254
Reference: [M1] Matsuoka, T.: The number and linking of periodic systems.Invent. Math. 70 (1983), 319–340. MR 0683687, 10.1007/BF01391795
Reference: [M2] Matsuoka, T.: Braids of periodic points and a $2$-dimensional analogue of Sharkovskii’s ordering.In: Dynamical Systems and Nonlinear Oscillations (G. Ikegami, ed.), World Sci. Press, Singapore 1986, 58–72. MR 0854304
Reference: [O] Orlicz, W.: Zur Theorie der Differentialgleichung ${y^{\prime }=f(x,y)}$.Bull. Akad. Polon. Sci., Sér. A, 00 (1932), 221–228.
Reference: [P] Pliss, V. A.: Nelokaľnyje problemy teorii kolebanij.Nauka, Moskva 1964. MR 0171962
Reference: [R] Robinson, C.: Dynamical Systems.CRC Press, Boca Raton, Fl. 1995. Zbl 0853.58001, MR 1396532
Reference: [S] Schirmer, H.: A topologist’s view of Sharkovsky’s theorem.Houston J. Math. 11, 3 (1985), 385–395. Zbl 0606.54031, MR 0808654
Reference: [Š] Šarkovskij, A. N.: Sosuščestvovanije ciklov nepreryvnogo otobraženija v sebja.Ukrain. Matem. Žurn. 1 (1964), 61–71.
Reference: [Y] Ye, X.: D-function of a minimal set and an extension of Sharkovskii’s theorem to minimal sets.Ergod. Th. Dynam. Sys. 12 (1992), 365–376. Zbl 0738.54019, MR 1176630
Reference: [Z1] Zgliczynski, P.: Sharkovskii theorem for multidimensional perturbations of oned̄imensional maps I, II.Ergod. Th. Dynam. Sys. 19, 6 (1999), 1655–1684; Topol. Meth. Nonlin. Anal. 14, 1 (1999), 169–182. 10.1017/S0143385799141749
Reference: [Z2] Zgliczynski, P.: Multidimensional perturbations of one-dimensional maps and stability of Šarkovskii ordering.Internat. J. Bifurc. Chaos 9, 9 (1999), 1867–1876. Zbl 1089.37502, MR 1728745, 10.1142/S0218127499001346
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