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An ergodic theory approach to chaos
Transitive dendrite map with infinite decomposition ideal
1. | Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica |
References:
[1] |
G. Acosta, R. Hernández-Gutiérrez, I. Naghmouchi and P. Oprocha, Periodic points and transitivity on dendrites, preprint, arXiv:1312.7426v1. |
[2] |
L. Alsedà, S. Kolyada, J. Llibre and L'. Snoha, Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc., 351 (1999), 1551-1573.
doi: 10.1090/S0002-9947-99-02077-2. |
[3] |
S. Baldwin, Entropy estimates for transitive maps on trees, Topology, 40 (2001), 551-569.
doi: 10.1016/S0040-9383(99)00074-9. |
[4] |
F. Balibrea and L'. Snoha, Topological entropy of Devaney chaotic maps, Topology Appl., 133 (2003), 225-239.
doi: 10.1016/S0166-8641(03)00090-7. |
[5] |
J. Banks, Regular periodic decompositions for topologically transitive maps, Ergodic Theory Dynam. Systems, 17 (1997), 505-529.
doi: 10.1017/S0143385797069885. |
[6] |
A. M. Blokh, On transitive mappings of one-dimensional branched manifolds (Russian), Differential-difference equations and problems of mathematical physics (Russian), 3-9, 131, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1984. |
[7] |
R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414; erratum: Trans. Amer. Math. Soc., 181 (1973), 509-510.
doi: 10.1090/S0002-9947-1971-0274707-X. |
[8] |
M. Dirbák, L'. Snoha and V. Špitalský, Minimality, transitivity, mixing and topological entropy on spaces with a free interval, Ergodic Theory Dynam. Systems, 33 (2013), 1786-1812.
doi: 10.1017/S0143385712000442. |
[9] |
L. Hoehn and C. Mouron, Hierarchies of chaotic maps on continua, Ergodic Theory Dynam. Systems, (2013), 1-17.
doi: 10.1017/etds.2013.32. |
[10] |
K. Kuratowski, Topology. Vol. II, Academic Press, New York-London, Państwowe Wydawnictwo Naukowe Polish Scientific Publishers, Warsaw, 1968. |
[11] |
S. B. Nadler, Continuum Theory. An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York, 1992. |
[12] |
P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
show all references
References:
[1] |
G. Acosta, R. Hernández-Gutiérrez, I. Naghmouchi and P. Oprocha, Periodic points and transitivity on dendrites, preprint, arXiv:1312.7426v1. |
[2] |
L. Alsedà, S. Kolyada, J. Llibre and L'. Snoha, Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc., 351 (1999), 1551-1573.
doi: 10.1090/S0002-9947-99-02077-2. |
[3] |
S. Baldwin, Entropy estimates for transitive maps on trees, Topology, 40 (2001), 551-569.
doi: 10.1016/S0040-9383(99)00074-9. |
[4] |
F. Balibrea and L'. Snoha, Topological entropy of Devaney chaotic maps, Topology Appl., 133 (2003), 225-239.
doi: 10.1016/S0166-8641(03)00090-7. |
[5] |
J. Banks, Regular periodic decompositions for topologically transitive maps, Ergodic Theory Dynam. Systems, 17 (1997), 505-529.
doi: 10.1017/S0143385797069885. |
[6] |
A. M. Blokh, On transitive mappings of one-dimensional branched manifolds (Russian), Differential-difference equations and problems of mathematical physics (Russian), 3-9, 131, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1984. |
[7] |
R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414; erratum: Trans. Amer. Math. Soc., 181 (1973), 509-510.
doi: 10.1090/S0002-9947-1971-0274707-X. |
[8] |
M. Dirbák, L'. Snoha and V. Špitalský, Minimality, transitivity, mixing and topological entropy on spaces with a free interval, Ergodic Theory Dynam. Systems, 33 (2013), 1786-1812.
doi: 10.1017/S0143385712000442. |
[9] |
L. Hoehn and C. Mouron, Hierarchies of chaotic maps on continua, Ergodic Theory Dynam. Systems, (2013), 1-17.
doi: 10.1017/etds.2013.32. |
[10] |
K. Kuratowski, Topology. Vol. II, Academic Press, New York-London, Państwowe Wydawnictwo Naukowe Polish Scientific Publishers, Warsaw, 1968. |
[11] |
S. B. Nadler, Continuum Theory. An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York, 1992. |
[12] |
P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
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