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August  2011, 30(3): 767-777. doi: 10.3934/dcds.2011.30.767

## On extensions of transitive maps

 1 Institute of Mathematics, NASU, Tereshchenkivs'ka 3, 01601 Kyiv, Ukraine 2 National Taras Shevchenko University of Kyiv, Faculty of Mechanics and Mathematics, bul. 7, 2, Academician Glushkov pr., 03127, Kyiv, Ukraine

Received  August 2009 Revised  January 2011 Published  March 2011

For a continuous selfmap $f$ of a compact metric space $X$ we study the set of its continuous extensions $F$ on the space $X\times I$, where $I$ is a compact interval. In particular, we have solved an open problem (raised in [Ll. Alseda, S. Kolyada, J. Llibre, and L. Snoha, Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc. 351 (1999)]) by proving that any continuous transitive map $f$ on $X$ can be extended to a continuous transitive triangular map $F=(f,g_x)$ on $X\times I$ without increasing topological entropy.
Citation: Sergiĭ Kolyada, Mykola Matviichuk. On extensions of transitive maps. Discrete & Continuous Dynamical Systems, 2011, 30 (3) : 767-777. doi: 10.3934/dcds.2011.30.767
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##### References:
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