On the dynamics of subcontinua of a tree

References

• Acosta , G. , Illanes , A. and Mendez-Lango , H. 2009 . The transitivity of induced maps . Topol. Appl. , 156 : 1013 – 1033 .
   Web of Science ®Google Scholar
• Adler , R. , Konheim , A. and McAndrew , J. 1965 . Topological entropy . Trans. Amer. Math. Soc. , 114 : 309 – 319 .
   Web of Science ®Google Scholar
• Alsedà , Ll. , Llibre , J. and Misiurewicz , M. 1993 . “ Combinatorial dynamics and entropy in dimension one ” . In Advanced Series in Nonlinear Dynamics , Vol. 5 , xiv+329 River Edge, NJ : World Scientific Publishing Co., Inc. .
   Google Scholar
• Auslander , J. , Kolyada , S. and Snoha , L. 2007 . Functional envelope of a dynamical system . Nonlinearity , 20 ( 9 ) : 2245 – 2269 .
   Web of Science ®Google Scholar
• Banks , J. 2005 . Chaos for induced hyperspace maps . Chaos Solitons Fractals , 25 : 681 – 685 .
   Web of Science ®Google Scholar
• Bowen , R. 1971 . Entropy for group endomorphisms and homogeneous spaces . Trans. Amer. Math. Soc. , 153 : 401 – 414 .
   Web of Science ®Google Scholar
• Fedorenko , V.V. 2004 . Topological limit of trajectories of intervals of one-dimensional dynamical systems . Grazer Math. Ber. , 346 : 107 – 111 . Proc. ECIT'02. J. Sousa Ramos, D. Gronau, C. Mira, L. Reich, A.N. Sharkovsky
   Google Scholar
• Fedorenko , V.V. , Romanenko , E.Yu. and Sharkovsky , A.N. 2007 . Trajectories of intervals in one-dimensional dynamical systems . J. Differ. Equ. Appl. , 13 ( 8–9 ) : 821 – 828 .
   Web of Science ®Google Scholar
• Glasner , E. and Weiss , B. 1995 . Quasi-factors of zero-entropy systems . J. Amer. Math. Soc. , 8 ( 3 ) : 665 – 686 .
   Web of Science ®Google Scholar
• Kolyada , S.F. 2004 . Topological entropy of a dynamical system on the space of one-dimensional maps (Ukrainian) . Neliniĭni Koliv. , 7 ( 2 ) : 180 – 187 . translation: Nonlin. Oscillations 7(1) (2004), pp. 83–89
   Google Scholar
• Kwietniak , D. and Oprocha , P. 2007 . Topological entropy and chaos for maps induced on hyperspaces . Chaos Solitons Fractals , 33 : 76 – 86 .
   Web of Science ®Google Scholar
• Matviichuk , M. 2009 . Entropy of induced maps for one-dimensional dynamics . Grazer Math. Ber. , 354 Proc. ECIT '08, 180–185, A.N. Sharkovsky, I.M. Sushko
   Google Scholar
• Romanenko , E.Yu. 2003 . Dynamical systems induced by continuous time difference equations and long-time behavior of solutions . J. Differ. Equ. Appl. , 9 ( 3–4 ) : 263 – 280 .
   Web of Science ®Google Scholar
• Sharkovsky , A.N. , Maystrenko , Yu.L. and Romanenko , E.Yu. 1993 . “ Difference equations and their applications ” . In Mathematics and its Applications , Vol. 250 , xii+358 Dordrecht : Kluwer Academic Publishers Group .
   Google Scholar
• Sharkovsky , A.N. and Romanenko , E.Yu. 2004 . Difference equations and dynamical systems generated by certain classes of boundary value problems . Proc. Steklov Inst. Math. , 244 : 264 – 279 .
   Google Scholar