Title:
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Šarkovského věta a diferenciální rovnice (Czech) |
Title:
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Sharkovkii theorem and differential equations (English) |
Author:
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Andres, Jan |
Language:
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Czech |
Journal:
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Pokroky matematiky, fyziky a astronomie |
ISSN:
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0032-2423 |
Volume:
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49 |
Issue:
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2 |
Year:
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2004 |
Pages:
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151-159 |
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Category:
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math |
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Keyword:
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Sharkovkii theorem |
Keyword:
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first order nonlinear differential equations |
MSC:
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34C25 |
MSC:
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37C10 |
MSC:
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37E15 |
MSC:
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39A99 |
MSC:
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58F20 |
idZBL:
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Zbl 1265.37016 |
. |
Date available:
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2010-12-11T20:28:38Z |
Last updated:
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2015-11-29 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/141221 |
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Related article:
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http://dml.cz/handle/10338.dmlcz/147803 |
Related article:
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http://dml.cz/handle/10338.dmlcz/141710 |
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Reference:
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[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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