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1. | Department of Mathematics, Baylor University, Waco, TX 76798-7328, United States, United States |
References:
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doi: 10.1023/A:1026775906693. |
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A. D. Barwell, C. Good, R. Knight and B. E. Raines, A characterization of $\omega$-limit sets in shift spaces, Ergodic Theory Dynam. Systems, 30 (2010), 21-31.
doi: 10.1017/S0143385708001089. |
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A. D. Barwell, A characterization of $\omega$-limit sets of piecewise monotone maps of the interval, Fund. Math., 207 (2010), 161-174.
doi: 10.4064/fm207-2-4. |
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A. D. Barwell, C. Good, P. Oprocha and B. E. Raines, Characterizations of $\omega$-limit sets of topologically hyperbolic spaces, Discrete Contin. Dyn. Syst., 33 (2013), 1819-1833.
doi: 10.3934/dcds.2013.33.1819. |
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W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, American Mathematical Society, Providence, R. I., 1955. |
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M. W. Hirsch, H.L. Smith and X. Q. Zhao, Chain transitivity, attractivity, and strong repellors for semidynamical systems, J. Dynam. Differential Equations, 13 (2001), 107-131.
doi: 10.1023/A:1009044515567. |
[7] |
M. Hochman, On the dynamics and recursive properties of multidimensional symbolic systems, Invent. Math., 176 (2009), 131-167.
doi: 10.1007/s00222-008-0161-7. |
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M. Hochman and T. Meyerovitch, A characterization of the entropies of multidimensional shifts of finite type, Ann. of Math. (2), 171 (2010), 2011-2038.
doi: 10.4007/annals.2010.171.2011. |
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A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995. |
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D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511626302. |
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P. Oprocha, Chain recurrence in multidimensional time discrete dynamical systems, Discrete Contin. Dyn. Syst., 20 (2008), 1039-1056.
doi: 10.3934/dcds.2008.20.1039. |
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P. Oprocha, Shadowing in multi-dimensional shift spaces, Colloq. Math., 110 (2008), 451-460.
doi: 10.4064/cm110-2-8. |
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P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. |
show all references
References:
[1] |
F. Balibrea and C. La Paz, A characterization of the $\omega$-limit sets of interval maps, Acta Math. Hungar., 88 (2000), 291-300.
doi: 10.1023/A:1026775906693. |
[2] |
A. D. Barwell, C. Good, R. Knight and B. E. Raines, A characterization of $\omega$-limit sets in shift spaces, Ergodic Theory Dynam. Systems, 30 (2010), 21-31.
doi: 10.1017/S0143385708001089. |
[3] |
A. D. Barwell, A characterization of $\omega$-limit sets of piecewise monotone maps of the interval, Fund. Math., 207 (2010), 161-174.
doi: 10.4064/fm207-2-4. |
[4] |
A. D. Barwell, C. Good, P. Oprocha and B. E. Raines, Characterizations of $\omega$-limit sets of topologically hyperbolic spaces, Discrete Contin. Dyn. Syst., 33 (2013), 1819-1833.
doi: 10.3934/dcds.2013.33.1819. |
[5] |
W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, American Mathematical Society, Providence, R. I., 1955. |
[6] |
M. W. Hirsch, H.L. Smith and X. Q. Zhao, Chain transitivity, attractivity, and strong repellors for semidynamical systems, J. Dynam. Differential Equations, 13 (2001), 107-131.
doi: 10.1023/A:1009044515567. |
[7] |
M. Hochman, On the dynamics and recursive properties of multidimensional symbolic systems, Invent. Math., 176 (2009), 131-167.
doi: 10.1007/s00222-008-0161-7. |
[8] |
M. Hochman and T. Meyerovitch, A characterization of the entropies of multidimensional shifts of finite type, Ann. of Math. (2), 171 (2010), 2011-2038.
doi: 10.4007/annals.2010.171.2011. |
[9] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995. |
[10] |
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511626302. |
[11] |
P. Oprocha, Chain recurrence in multidimensional time discrete dynamical systems, Discrete Contin. Dyn. Syst., 20 (2008), 1039-1056.
doi: 10.3934/dcds.2008.20.1039. |
[12] |
P. Oprocha, Shadowing in multi-dimensional shift spaces, Colloq. Math., 110 (2008), 451-460.
doi: 10.4064/cm110-2-8. |
[13] |
P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. |
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