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Topological properties of sectional-Anosov flows
Transitive sofic spacing shifts
1. | Department of Mathematics and Statistics, University of Melbourne, Parkville 3010, Australia |
2. | Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków |
3. | Department of Mathematics and Statistics, La Trobe University, Bundoora 3086, Australia |
References:
[1] |
D. Ahmadi and M. Dabbaghian, Characterization of spacing shifts with positive topological entropy, Acta Math. Univ. Comenian. (N.S.), 81 (2012), 221-226. |
[2] |
N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems. Recent Advances, North-Holland Mathematical Library, 52, North-Holland Publishing Co., Amsterdam, 1994. |
[3] |
J. Banks, Regular Periodic Decompositions for Topologically Transitive maps, Ergodic Theory Dynam. Systems 17 (1997), 505-529.
doi: 10.1017/S0143385797069885. |
[4] |
J. Banks, T. T. D. Nguyen, P. Oprocha, B. Stanley and B. Trotta, Dynamics of spacing shifts, Discrete Contin. Dyn. Syst. 33 (2013), 4207-4232.
doi: 10.3934/dcds.2013.33.4207. |
[5] |
D. S. Dummit and R. M. Foote, Abstract Algebra, Third edition, John Wiley & Sons, Inc., Hoboken, NJ, 2004. |
[6] |
H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, N.J., 1981. |
[7] |
S. Ginsburg, Algebraic and automata-theoretic properties of formal languages, North-Holland/American Elsevier, 1975. |
[8] |
M. Harrison, Introduction to Formal Language Theory, Addison-Wesley, 1978. |
[9] |
D. Kwietniak, Topological entropy and distributional chaos in hereditary shifts with applications to spacing shifts and beta shifts, Discrete Contin. Dyn. Syst, 33 (2013), 2451-2467.
doi: 10.3934/dcds.2013.33.2451. |
[10] |
K. Lau and A. Zame, On weak mixing of cascades, Math. Systems Theory, 6 (1973), 307-311.
doi: 10.1007/BF01740722. |
[11] |
D. Lind and B. Marcus, Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511626302. |
[12] |
M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, 1997.
doi: 10.1017/CBO9780511566097. |
show all references
References:
[1] |
D. Ahmadi and M. Dabbaghian, Characterization of spacing shifts with positive topological entropy, Acta Math. Univ. Comenian. (N.S.), 81 (2012), 221-226. |
[2] |
N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems. Recent Advances, North-Holland Mathematical Library, 52, North-Holland Publishing Co., Amsterdam, 1994. |
[3] |
J. Banks, Regular Periodic Decompositions for Topologically Transitive maps, Ergodic Theory Dynam. Systems 17 (1997), 505-529.
doi: 10.1017/S0143385797069885. |
[4] |
J. Banks, T. T. D. Nguyen, P. Oprocha, B. Stanley and B. Trotta, Dynamics of spacing shifts, Discrete Contin. Dyn. Syst. 33 (2013), 4207-4232.
doi: 10.3934/dcds.2013.33.4207. |
[5] |
D. S. Dummit and R. M. Foote, Abstract Algebra, Third edition, John Wiley & Sons, Inc., Hoboken, NJ, 2004. |
[6] |
H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, N.J., 1981. |
[7] |
S. Ginsburg, Algebraic and automata-theoretic properties of formal languages, North-Holland/American Elsevier, 1975. |
[8] |
M. Harrison, Introduction to Formal Language Theory, Addison-Wesley, 1978. |
[9] |
D. Kwietniak, Topological entropy and distributional chaos in hereditary shifts with applications to spacing shifts and beta shifts, Discrete Contin. Dyn. Syst, 33 (2013), 2451-2467.
doi: 10.3934/dcds.2013.33.2451. |
[10] |
K. Lau and A. Zame, On weak mixing of cascades, Math. Systems Theory, 6 (1973), 307-311.
doi: 10.1007/BF01740722. |
[11] |
D. Lind and B. Marcus, Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511626302. |
[12] |
M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, 1997.
doi: 10.1017/CBO9780511566097. |
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