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SHARKOVSKII'S THEOREM FOR CONNECTIVITY G_δ-RELATIONS

Department of Mathematics Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic

Supported by the Council of Czech Government (MSM 6198959214).

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PAVLA ŠNYRYCHOVÁ

Department of Mathematics Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic

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, and

PIOTR SZUCA

Department of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

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https://doi.org/10.1142/S0218127406016136Cited by:3 (Source: Crossref)

Abstract

A version of Sharkovskii's cycle coexistence theorem is formulated for a composition of connectivity G_δ-relations with closed values. Thus, a multivalued version in [Andres & Pastor, 2005] holding with at most two exceptions for M-maps, jointly with a single-valued version in [Szuca, 2003], for functions with a connectivity G_δ-graph, are generalized. In particular, our statement is applicable to differential inclusions as well as to some discontinuous functions.

Keywords:

References

L. Alsedà, J. Llibre and M. Misiurewicz, Int. J. Bifurcation and Chaos 9, 1687 (1999), DOI: 10.1142/S0218127499001188. Link, Web of Science, Google Scholar
J. Andres, J. Fišer and L. Jütner, Set-Val. Anal. 10, 1 (2002). Crossref, Web of Science, Google Scholar
J. Andres and L. Jütner, Nonlin. Anal. 51, 1101 (2002), DOI: 10.1016/S0362-546X(01)00876-8. Crossref, Web of Science, Google Scholar
J. Andres and L. Górniewicz , Topological Fixed Point Principles for Boundary Value Problems ( Kluwer , Dordrecht , 2003 ) . Crossref, Google Scholar
J. Andres and K. Pastor, Topol. Meth. Nonlin. Anal. 22, 369 (2003). Crossref, Google Scholar
J. Andres, J. Diff. Eqns. Appl. 10, 17 (2004). Crossref, Web of Science, Google Scholar
J. Andres, L. Jütner and K. Pastor, Set-Val. Anal. 13, 47 (2005). Crossref, Web of Science, Google Scholar
J. Andres and K. Pastor, Proc. Am. Math. Soc. 133, 449 (2005), DOI: 10.1090/S0002-9939-04-07627-0. Crossref, Web of Science, Google Scholar
C. Bernhardt, J. Diff. Eqns. Appl. 10, 29 (2004). Crossref, Web of Science, Google Scholar
K. Kellum, Real Anal. Exch. 14, 420 (1989). Crossref, Google Scholar
T. Li and J. A. Yorke, Amer. Math. Monthly 82, 985 (1975). Crossref, Web of Science, Google Scholar
C. Robinson , Dynamical Systems ( CRC Press , Boca Raton , 1995 ) . Google Scholar
A. N. Sharkovskii, Ukrain. Math. J. 16, 61 (1964). Web of Science, Google Scholar
A. N. Sharkovskii, Int. J. Bifurcation and Chaos 5, 1263 (1995), DOI: 10.1142/S0218127495000934. Link, Web of Science, Google Scholar
P. Szuca, Fund. Math. 179, 27 (2003). Crossref, Web of Science, Google Scholar
P. Szuca, Real Anal. Exch. 29, 205 (2004). Crossref, Google Scholar