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Hyperbolic sets and entropy at the homological level
Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval
1. | Mathematical Institute, Silesian University, 746 01 Opava |
References:
[1] |
A. M. Bruckner and J. Smítal, A characterization of $\omega$-limit sets of maps of the interval with zero topological entropy, Ergodic Theory & Dynam. Systems, 13 (1993), 7-19.
doi: 10.1017/S0143385700007173. |
[2] |
J. Cánovas, Li-Yorke chaos in a class of nonautonomous discrete systems, J. Difference Equ. Appl., 17 (2011), 479-486.
doi: 10.1080/10236190903049025. |
[3] |
T. Downarowicz, Positive entropy implies distributional chaos DC2, Proc. Amer. Math. Soc., 142 (2014), 137-149.
doi: 10.1090/S0002-9939-2013-11717-X. |
[4] |
J. Dvořáková, Chaos in nonautonomous discrete dynamical systems, Commun. Nonlin. Sci. Numer. Simulat., 17 (2012), 4649-4652.
doi: 10.1016/j.cnsns.2012.06.005. |
[5] |
V. V. Fedorenko, A. N. Šarkovskii and J. Smítal, Characterizations of weakly chaotic maps of the interval, Proc. Amer. Math. Soc., 110 (1990), 141-148.
doi: 10.1090/S0002-9939-1990-1017846-5. |
[6] |
G.-L. Forti, L. Paganoni and J. Smítal, Dynamics of homeomorphisms on minimal sets generated by triangular mappings, Bull. Austral. Math. Soc., 59 (1999), 1-20.
doi: 10.1017/S000497270003255X. |
[7] |
S. Kolyada and L. Snoha, Topological entropy of nonautonomous dynamical systems, Random & Comput. Dynamics, 4 (1996), 205-233. |
[8] |
M. Kuchta, Shadowing property of continuous maps with zero topological entropy, Proc. Amer. Math. Soc., 119 (1993), 641-648.
doi: 10.1090/S0002-9939-1993-1165058-X. |
[9] |
M. Misiurewicz and J. Smítal, Smooth chaotic maps with zero topological entropy, Ergodic Theory & Dynam. Systems, 8 (1988), 421-424.
doi: 10.1017/S0143385700004557. |
[10] |
A. N. Šarkovskii, Attracting sets containing no cycles, Ukrain. Mat. Ž., 20 (1968), 136-142. |
[11] |
B. Schweizer and J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc., 344 (1994), 737-754.
doi: 10.1090/S0002-9947-1994-1227094-X. |
[12] |
J. Smítal, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc., 297 (1986), 269-282.
doi: 10.1090/S0002-9947-1986-0849479-9. |
[13] |
J. Smítal and M. Štefánková, Distributional chaos for triangular maps, Chaos, Solitons and Fractals, 21 (2004), 1125-1128.
doi: 10.1016/j.chaos.2003.12.105. |
show all references
References:
[1] |
A. M. Bruckner and J. Smítal, A characterization of $\omega$-limit sets of maps of the interval with zero topological entropy, Ergodic Theory & Dynam. Systems, 13 (1993), 7-19.
doi: 10.1017/S0143385700007173. |
[2] |
J. Cánovas, Li-Yorke chaos in a class of nonautonomous discrete systems, J. Difference Equ. Appl., 17 (2011), 479-486.
doi: 10.1080/10236190903049025. |
[3] |
T. Downarowicz, Positive entropy implies distributional chaos DC2, Proc. Amer. Math. Soc., 142 (2014), 137-149.
doi: 10.1090/S0002-9939-2013-11717-X. |
[4] |
J. Dvořáková, Chaos in nonautonomous discrete dynamical systems, Commun. Nonlin. Sci. Numer. Simulat., 17 (2012), 4649-4652.
doi: 10.1016/j.cnsns.2012.06.005. |
[5] |
V. V. Fedorenko, A. N. Šarkovskii and J. Smítal, Characterizations of weakly chaotic maps of the interval, Proc. Amer. Math. Soc., 110 (1990), 141-148.
doi: 10.1090/S0002-9939-1990-1017846-5. |
[6] |
G.-L. Forti, L. Paganoni and J. Smítal, Dynamics of homeomorphisms on minimal sets generated by triangular mappings, Bull. Austral. Math. Soc., 59 (1999), 1-20.
doi: 10.1017/S000497270003255X. |
[7] |
S. Kolyada and L. Snoha, Topological entropy of nonautonomous dynamical systems, Random & Comput. Dynamics, 4 (1996), 205-233. |
[8] |
M. Kuchta, Shadowing property of continuous maps with zero topological entropy, Proc. Amer. Math. Soc., 119 (1993), 641-648.
doi: 10.1090/S0002-9939-1993-1165058-X. |
[9] |
M. Misiurewicz and J. Smítal, Smooth chaotic maps with zero topological entropy, Ergodic Theory & Dynam. Systems, 8 (1988), 421-424.
doi: 10.1017/S0143385700004557. |
[10] |
A. N. Šarkovskii, Attracting sets containing no cycles, Ukrain. Mat. Ž., 20 (1968), 136-142. |
[11] |
B. Schweizer and J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc., 344 (1994), 737-754.
doi: 10.1090/S0002-9947-1994-1227094-X. |
[12] |
J. Smítal, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc., 297 (1986), 269-282.
doi: 10.1090/S0002-9947-1986-0849479-9. |
[13] |
J. Smítal and M. Štefánková, Distributional chaos for triangular maps, Chaos, Solitons and Fractals, 21 (2004), 1125-1128.
doi: 10.1016/j.chaos.2003.12.105. |
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