Period Three Implications for Expansive Maps in ℝN

Journal of Difference Equations and Applications

Volumn 10, Issue 1, 2004, Pages 17-28

  Andres, Jan ^a  

^a PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

Expansive maps; Li Yorke's theorem; Multidimensional version; Period three implications; Periodic points

Indexed keywords

EID: 0842325144     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/1023619031000114314     Document Type: Article

References (28)

1. K. T. Alligood, T. D. Sauer and J. A. Yorke, Chaos (An Introduction to Dynamical Systems), Springer, Berlin, 1997.
2. J. Andres, Nielsen number, Artin braids, Poincaré operators and multiple nonlinear oscillations, Nonlin. Anal., 47(2) (2001), 1017-1028.
3. J. Andres, J. Fiser and L. Jüttner, On a multivalued version of the Sharkovskii theorem and its application to differential inclusions, Set-Valued Anal., 10(1) (2002), 1-14.
4. Andres, J. and Jüttner, L., Period three plays a negative role in a multivalued version of Sharkovskii's theorem, Nonlin. Anal., 51 (2002), 1101-1104.
5. J. Andres, L. Jüttner, and K. Pastor, On a multivalued version of the Sharkovskii theorem and its application to differential inclusions, II, Submitted.
6. J. S. Bae, An example of a partially ordered Sharkovsky space, Bull. Korean Math. Soc., 27(2) (1990), 127-131.
7. A. I. Demin, Coexisting of periodic, almost-periodic and recurrent points of transformations of n -od, Vestnik Mask. Univ 1 (Matern. Mekh.), 3 (1996), 84-87 (in Russian).
8. J. Franks and M. Misiurewicz, In: C. K. McCord, ed, Cycles for disk homomorphisms and thick trees, Contemp. Math. 152 Nielsen Theory and Dynamical Systems, Amer. Math. Soc., Providence, RI, 1993, pp. 69-139.
9. J.-M. Gambaudo, S. van Strien and C. Tresser, Vers un ordre de Sharkovskii pour les plongements du disque préservant l'orientation, C.R. Acad. Sci. Paris, Sér. I Math., 310 (1990), 291-294.
10. L. Górniewicz, Toplogical Fixed Point Theory of Multivalued Mappings, Kluwer, Dordrecht, 1999.
11. J. Guaschi, Pseudo-Anosov braid types of the disc or sphere of the disc or sphere of low cardinality imply all periods, J. Lond. Math. Soc., 2(50) (1994), 594-608.
12. J. Guaschi, Nielsen theory, braids and fixed points of surface homomorphisms, Topol. Appl., 117 (2002), 199-230.
13. M. Handel, The forcing partial order on three times punctured disk, Ergod. Th. Dyn. Syst., 17 (1997), 593-610.
14. S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer, Dordrecht, 1997.
15. J. Kampen, On fixed points of maps and iterated maps and applications, Nonlin. Anal., 42 (2000), 509-532.
16. V. Kannan, P. V. S. P. Saradhi and S. P. Seshasai, A generalization of Sharkovskii theorem to higher dimensions, J. Nat. Acad. Math. India, 11 (1995), 69-82 (Special volume to dedicate Prof. Dr. R. S. Mishra on the occasion of his 80th birthday).
17. P. E. Kloeden, On Sharkovsky's cycle coexisting ordering, Bull. Aust. Math. Soc., 20 (1979), 171-177.
18. B. Kolev, Periodic points of period 3 in the disc, Nonlinearity, 7 (1994), 1067-1072.
19. T.-Y. Li and J. A. Yorke, Period three implies chaos, Am. Math. Monthly, 82 (1975), 985-992.
20. J. Llibre and R. S. MacKay, Pseudo-Anosov homeomorphisms on a sphere with four punctures have all periods, Math. Proc. Camb. Phil. Soc., 112 (1992), 539-550.
21. T. Matsuoka, Braids of periodic points and a 2-dimensional analogue of Sharkovskii's ordering", In: G. Ikegami, ed, Dynamical Systems and Nonlinear Oscillations, World Sci. Press, Singapore, 1986, pp. 58-72.
22. T. Matsuoka, The number and linking of periodic solutions of periodic systems, Invent. Math., 70 (1983), 319-340.
23. C. Robinson, Dynamical Systems (Stability, Symbolic Dynamics and Chaos), CRC Press, Boca Raton, FL, 1995.
24. H. Schirmer, A topologist's view of Sharkovsky's theorem, Houston J. Math., 11(3) (1985), 385-395.
25. A. N. Sharkovskii, Coexistence of cycles of a continuous map of a line into itself, Ukr. Math. J., 16 (1964), 61-71 (in Russian).
26. X. Ye, D-function of a minimal set and an extesion of Sharkovskii's theorem to minimal sets, Ergod. Th. Dyn. Syst., 12 (1992), 365-376.
27. P. Zgliczynski, Sharkovskii theorem for multidimensional perturbations of 1-dim maps, Ergod. Th. Dyn. Syst., 19(6) (1999), 1655-1684.
28. P. Zgliczynski, Sharkovskii theorem for multidimensional perturbations of one-dimensional maps, II, Topol. Math. Nonlin. Anal., 14(1) (1999), 169-182.