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On the integral systems with negative exponents
Recurrence properties and disjointness on the induced spaces
1. | Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, School of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China, China, China |
References:
[1] |
J. Auslander, Minimal Flows and Their Extensions,, North-Holland Mathematics Studies, 153 (1988).
|
[2] |
J. Banks, Regular periodic decompositions for topologically transitive maps,, Ergodic Th. and Dynam. Sys., 17 (1997), 505.
doi: 10.1017/S0143385797069885. |
[3] |
J. Banks, Chaos for induced hyperspace maps,, Chaos Solitons Fractals, 25 (2005), 681.
doi: 10.1016/j.chaos.2004.11.089. |
[4] |
W. Bauer and K. Sigmund, Topological dynamics of transformations induced on the space of probability measures,, Monatsh. Math., 79 (1975), 81.
doi: 10.1007/BF01585664. |
[5] |
A. Blokh and A. Fieldsteel, Sets that force recurrence,, Proc. Amer. Math. Soc., 130 (2002), 3571.
doi: 10.1090/S0002-9939-02-06349-9. |
[6] |
M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces,, Lecture Notes in Mathematics, 527 (1976).
doi: 10.1007/BFb0082364. |
[7] |
P. Dong, S. Shao and X. Ye, Product recurrent properties, disjointness and weak disjointness,, Israel J. of Math., 188 (2012), 463.
doi: 10.1007/s11856-011-0128-z. |
[8] |
H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation,, Math. Systems Theory , 1 (1967), 1.
doi: 10.1007/BF01692494. |
[9] |
H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory,, M. B. Porter Lectures, (1981).
|
[10] |
E. Glasner and B. Weiss, Quasi-factors of zero-entropy systems,, J. Amer. Math. Soc., 8 (1995), 665.
doi: 10.1090/S0894-0347-1995-1270579-5. |
[11] |
J. Guirao, K. Kwietniak, M. Lampart, P. Oprocha and A. Peris, Chaos on hyperspaces,, Nonlinear Anal., 71 (2009), 1.
doi: 10.1016/j.na.2008.10.055. |
[12] |
W. Huang, H. Li and X. Ye, Family independence for topological and measurable dynamics,, Trans. Amer. Math. Soc., 364 (2012), 5209.
doi: 10.1090/S0002-9947-2012-05493-6. |
[13] |
W. Huang, K. Park and X. Ye, Topological disjointness from entropy zero systems,, Bull. Soc. Math. France, 135 (2007), 259.
|
[14] |
W. Huang and X. Ye, Dynamical systems disjoint from any minimal system,, Trans. Amer. Math. Soc., 357 (2005), 669.
doi: 10.1090/S0002-9947-04-03540-8. |
[15] |
D. Kerr and H. Li, Dynamical entropy in Banach spaces,, Invent. Math., 162 (2005), 649.
doi: 10.1007/s00222-005-0457-9. |
[16] |
D. Kerr and H. Li, Independence in topological and $C^*$-dynamics,, Math. Ann., 338 (2007), 869.
doi: 10.1007/s00208-007-0097-z. |
[17] |
M. Komuro, The pseudo orbit tracing properties on the space of probability measures,, Tokyo J. Math., 7 (1984), 461.
doi: 10.3836/tjm/1270151738. |
[18] |
E. Lehrer, Topological mixing and uniquely ergodic systems,, Israel J. Math., 57 (1987), 239.
doi: 10.1007/BF02772176. |
[19] |
J. Li, Transitive points via Furstenberg family,, Topology Appl., 158 (2011), 2221.
doi: 10.1016/j.topol.2011.07.013. |
[20] |
J. Li, Equivalent conditions of Devaney chaos on the hyperspace,, J. Univ. Sci. Technol. China, 44 (2014), 93. Google Scholar |
[21] |
Z. Lian, S. Shao and X. Ye, Weakly mixing, proximal topological models for ergodic systems and applications,, preprint, (). Google Scholar |
[22] |
Sam B. Nadler, Jr., Continuum Theory: An Introduction,, Pure and Applied Mathematics, 158 (1992).
|
[23] |
P. Oprocha, Weak mixing and product recurrence,, Ann. Inst. Fourier (Grenoble), 60 (2010), 1233.
doi: 10.5802/aif.2553. |
[24] |
K. R. Parthasarathy, Probability Measures on Metric Spaces,, Probability and Mathematical Statistics, 3 (1967).
|
[25] |
K. Petersen, Disjointness and weak mixing of minimal sets,, Proc. Amer. Math. Soc., 24 (1970), 278.
doi: 10.1090/S0002-9939-1970-0250283-7. |
[26] |
H. Román-Flores, A note on transitivity in set-valued discrete systems,, Chaos Solitons Fractals, 17 (2003), 99.
doi: 10.1016/S0960-0779(02)00406-X. |
[27] |
S. Shao, Dynamical Systems and Families,, PhD thesis, (2003). Google Scholar |
[28] |
P. Walters, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, 79 (1982).
|
show all references
References:
[1] |
J. Auslander, Minimal Flows and Their Extensions,, North-Holland Mathematics Studies, 153 (1988).
|
[2] |
J. Banks, Regular periodic decompositions for topologically transitive maps,, Ergodic Th. and Dynam. Sys., 17 (1997), 505.
doi: 10.1017/S0143385797069885. |
[3] |
J. Banks, Chaos for induced hyperspace maps,, Chaos Solitons Fractals, 25 (2005), 681.
doi: 10.1016/j.chaos.2004.11.089. |
[4] |
W. Bauer and K. Sigmund, Topological dynamics of transformations induced on the space of probability measures,, Monatsh. Math., 79 (1975), 81.
doi: 10.1007/BF01585664. |
[5] |
A. Blokh and A. Fieldsteel, Sets that force recurrence,, Proc. Amer. Math. Soc., 130 (2002), 3571.
doi: 10.1090/S0002-9939-02-06349-9. |
[6] |
M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces,, Lecture Notes in Mathematics, 527 (1976).
doi: 10.1007/BFb0082364. |
[7] |
P. Dong, S. Shao and X. Ye, Product recurrent properties, disjointness and weak disjointness,, Israel J. of Math., 188 (2012), 463.
doi: 10.1007/s11856-011-0128-z. |
[8] |
H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation,, Math. Systems Theory , 1 (1967), 1.
doi: 10.1007/BF01692494. |
[9] |
H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory,, M. B. Porter Lectures, (1981).
|
[10] |
E. Glasner and B. Weiss, Quasi-factors of zero-entropy systems,, J. Amer. Math. Soc., 8 (1995), 665.
doi: 10.1090/S0894-0347-1995-1270579-5. |
[11] |
J. Guirao, K. Kwietniak, M. Lampart, P. Oprocha and A. Peris, Chaos on hyperspaces,, Nonlinear Anal., 71 (2009), 1.
doi: 10.1016/j.na.2008.10.055. |
[12] |
W. Huang, H. Li and X. Ye, Family independence for topological and measurable dynamics,, Trans. Amer. Math. Soc., 364 (2012), 5209.
doi: 10.1090/S0002-9947-2012-05493-6. |
[13] |
W. Huang, K. Park and X. Ye, Topological disjointness from entropy zero systems,, Bull. Soc. Math. France, 135 (2007), 259.
|
[14] |
W. Huang and X. Ye, Dynamical systems disjoint from any minimal system,, Trans. Amer. Math. Soc., 357 (2005), 669.
doi: 10.1090/S0002-9947-04-03540-8. |
[15] |
D. Kerr and H. Li, Dynamical entropy in Banach spaces,, Invent. Math., 162 (2005), 649.
doi: 10.1007/s00222-005-0457-9. |
[16] |
D. Kerr and H. Li, Independence in topological and $C^*$-dynamics,, Math. Ann., 338 (2007), 869.
doi: 10.1007/s00208-007-0097-z. |
[17] |
M. Komuro, The pseudo orbit tracing properties on the space of probability measures,, Tokyo J. Math., 7 (1984), 461.
doi: 10.3836/tjm/1270151738. |
[18] |
E. Lehrer, Topological mixing and uniquely ergodic systems,, Israel J. Math., 57 (1987), 239.
doi: 10.1007/BF02772176. |
[19] |
J. Li, Transitive points via Furstenberg family,, Topology Appl., 158 (2011), 2221.
doi: 10.1016/j.topol.2011.07.013. |
[20] |
J. Li, Equivalent conditions of Devaney chaos on the hyperspace,, J. Univ. Sci. Technol. China, 44 (2014), 93. Google Scholar |
[21] |
Z. Lian, S. Shao and X. Ye, Weakly mixing, proximal topological models for ergodic systems and applications,, preprint, (). Google Scholar |
[22] |
Sam B. Nadler, Jr., Continuum Theory: An Introduction,, Pure and Applied Mathematics, 158 (1992).
|
[23] |
P. Oprocha, Weak mixing and product recurrence,, Ann. Inst. Fourier (Grenoble), 60 (2010), 1233.
doi: 10.5802/aif.2553. |
[24] |
K. R. Parthasarathy, Probability Measures on Metric Spaces,, Probability and Mathematical Statistics, 3 (1967).
|
[25] |
K. Petersen, Disjointness and weak mixing of minimal sets,, Proc. Amer. Math. Soc., 24 (1970), 278.
doi: 10.1090/S0002-9939-1970-0250283-7. |
[26] |
H. Román-Flores, A note on transitivity in set-valued discrete systems,, Chaos Solitons Fractals, 17 (2003), 99.
doi: 10.1016/S0960-0779(02)00406-X. |
[27] |
S. Shao, Dynamical Systems and Families,, PhD thesis, (2003). Google Scholar |
[28] |
P. Walters, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, 79 (1982).
|
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