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Directional uniformities, periodic points, and entropy
Topological mixing, knot points and bounds of topological entropy
1. | Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków |
2. | AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland |
References:
[1] |
Ll. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One,, Second edition, (2000).
doi: 10.1142/4205. |
[2] |
M. Barge and J. Martin, Dense periodicity on the interval,, Proc. Amer. Math. Soc., 94 (1985), 731.
doi: 10.1090/S0002-9939-1985-0792293-8. |
[3] |
M. Barge and J. Martin, Dense orbits on the interval,, Michigan Math. J., 34 (1987), 3.
doi: 10.1307/mmj/1029003477. |
[4] |
A. Barrio Blaya and V. Jiménez López, On the relations between positive Lyapunov exponents, positive entropy, and sensitivity for interval maps,, Discrete Contin. Dyn. Syst., 32 (2012), 433.
doi: 10.3934/dcds.2012.32.433. |
[5] |
L. S. Block and W. A. Coppel, Dynamics in One Dimension,, Lecture Notes in Mathematics, (1513).
|
[6] |
L. Block and E. M. Coven, Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval,, Trans. Amer. Math. Soc., 300 (1987), 297.
doi: 10.1090/S0002-9947-1987-0871677-X. |
[7] |
J. Bobok, Strictly ergodic patterns and entropy for interval maps,, Acta Math. Univ. Comenianae, 72 (2003), 111.
|
[8] |
J. Bobok, The topological entropy versus level sets for interval maps. II, Studia Math., 166 (2005), 11.
doi: 10.4064/sm166-1-2. |
[9] |
J. Bobok and M. Soukenka, Irreducibility, infinite level sets, and small entropy,, Real Analysis Exchange, 36 (): 449.
|
[10] |
J. Bobok and Z. Nitecki, The topological entropy of $m$-fold maps,, Ergod. Th. Dynam. Sys., 25 (2005), 375.
doi: 10.1017/S0143385704000574. |
[11] |
A. Bruckner, Differentiation of Real Functions,, Second edition, (1994).
|
[12] |
G. Harańczyk and D. Kwietniak, When lower entropy implies stronger Devanay chaos,, Proceedings of the American Mathematical Society, 137 (2009), 2063.
doi: 10.1090/S0002-9939-08-09756-6. |
[13] |
G. W. Henderson, The pseudo-arc as an inverse limit with one binding map,, Duke Math. J., 31 (1964), 421.
doi: 10.1215/S0012-7094-64-03140-0. |
[14] |
P. Kościelniak and P. Oprocha, Shadowing, entropy and a homeomorphism of the pseudoarc,, Proc. Amer. Math. Soc., 138 (2010), 1047.
doi: 10.1090/S0002-9939-09-10162-4. |
[15] |
P. Kůrka, Topological and Symbolic Dynamics,, Cours Spécialisés [Specialized Courses], (2003).
|
[16] |
R. Mañé, Ergodic Theory and Differentiable Dynamics,, Springer, (1987).
doi: 10.1007/978-3-642-70335-5. |
[17] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings,, Studia Math., 67 (1980), 45.
|
[18] |
C. Mouron, Entropy of shift maps of the pseudo-arc,, Topology Appl., 159 (2012), 34.
doi: 10.1016/j.topol.2011.07.014. |
[19] |
S. Ruette, Chaos for continuous interval maps, preprint,, 2003. Available from: , (). Google Scholar |
[20] |
P. Walters, An Introduction to Ergodic Theory,, Springer, (1982).
|
show all references
References:
[1] |
Ll. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One,, Second edition, (2000).
doi: 10.1142/4205. |
[2] |
M. Barge and J. Martin, Dense periodicity on the interval,, Proc. Amer. Math. Soc., 94 (1985), 731.
doi: 10.1090/S0002-9939-1985-0792293-8. |
[3] |
M. Barge and J. Martin, Dense orbits on the interval,, Michigan Math. J., 34 (1987), 3.
doi: 10.1307/mmj/1029003477. |
[4] |
A. Barrio Blaya and V. Jiménez López, On the relations between positive Lyapunov exponents, positive entropy, and sensitivity for interval maps,, Discrete Contin. Dyn. Syst., 32 (2012), 433.
doi: 10.3934/dcds.2012.32.433. |
[5] |
L. S. Block and W. A. Coppel, Dynamics in One Dimension,, Lecture Notes in Mathematics, (1513).
|
[6] |
L. Block and E. M. Coven, Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval,, Trans. Amer. Math. Soc., 300 (1987), 297.
doi: 10.1090/S0002-9947-1987-0871677-X. |
[7] |
J. Bobok, Strictly ergodic patterns and entropy for interval maps,, Acta Math. Univ. Comenianae, 72 (2003), 111.
|
[8] |
J. Bobok, The topological entropy versus level sets for interval maps. II, Studia Math., 166 (2005), 11.
doi: 10.4064/sm166-1-2. |
[9] |
J. Bobok and M. Soukenka, Irreducibility, infinite level sets, and small entropy,, Real Analysis Exchange, 36 (): 449.
|
[10] |
J. Bobok and Z. Nitecki, The topological entropy of $m$-fold maps,, Ergod. Th. Dynam. Sys., 25 (2005), 375.
doi: 10.1017/S0143385704000574. |
[11] |
A. Bruckner, Differentiation of Real Functions,, Second edition, (1994).
|
[12] |
G. Harańczyk and D. Kwietniak, When lower entropy implies stronger Devanay chaos,, Proceedings of the American Mathematical Society, 137 (2009), 2063.
doi: 10.1090/S0002-9939-08-09756-6. |
[13] |
G. W. Henderson, The pseudo-arc as an inverse limit with one binding map,, Duke Math. J., 31 (1964), 421.
doi: 10.1215/S0012-7094-64-03140-0. |
[14] |
P. Kościelniak and P. Oprocha, Shadowing, entropy and a homeomorphism of the pseudoarc,, Proc. Amer. Math. Soc., 138 (2010), 1047.
doi: 10.1090/S0002-9939-09-10162-4. |
[15] |
P. Kůrka, Topological and Symbolic Dynamics,, Cours Spécialisés [Specialized Courses], (2003).
|
[16] |
R. Mañé, Ergodic Theory and Differentiable Dynamics,, Springer, (1987).
doi: 10.1007/978-3-642-70335-5. |
[17] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings,, Studia Math., 67 (1980), 45.
|
[18] |
C. Mouron, Entropy of shift maps of the pseudo-arc,, Topology Appl., 159 (2012), 34.
doi: 10.1016/j.topol.2011.07.014. |
[19] |
S. Ruette, Chaos for continuous interval maps, preprint,, 2003. Available from: , (). Google Scholar |
[20] |
P. Walters, An Introduction to Ergodic Theory,, Springer, (1982).
|
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