`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Measurable sensitivity via Furstenberg families
Pages: 4543 - 4563, Issue 8, August 2017

doi:10.3934/dcds.2017194      Abstract        References        Full text (472.8K)           Related Articles

Tao Yu - Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China (email)

1 C. Abraham, G. Biau and B. Cadre, Chaotic properties of mappings on a probability space, J. Math. Anal. Appl., 266 (2002), 420-431.       
2 E. Akin and S. Kolyada, Li-Yorke sensitivity, Nonlinearity, 16 (2003), 1421-1433.       
3 J. Auslander, Minimal Flows and Their Extensions, North-Holland Mathematics Studies 153, Elsevier, 1988.       
4 J. Auslander and J. A. Yorke, Interval maps, factors of maps, and chaos, Tôhoku Math. J. (2), 32 (1980), 177-188.       
5 V. Bergelson, Ultrafilters, IP sets, dynamics, and combinatorial number theory, Ultrafilters Across Mathematics, 23-47, Contemp. Math., 530, Amer. Math. Soc., Providence, RI, 2010.       
6 B. Cadre and P. Jacob, On pairwise sensitivity, J. Math. Anal. Appl., 309 (2005), 375-382.       
7 P. Dong, S. Donoso, A. Maass, S. Shao and X. Ye, Infinite-step nilsystems, independence and complexity, Ergodic Theory Dynam. Systems, 33 (2013), 118-143.       
8 T. Downarowicz and E. Glasner, Isomorphic extension and applications, Topol. Methods Nonlinear Anal., 48 (2016), 321-338.       
9 T. Downarowicz and S. Kasjan, Odometers and toeplitz systems revisited in the context of sarnak's conjecture, Studia Math., 229 (2015), 45-72, arXiv:1502.02307.       
10 H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, M. B. Porter Lectures. Princeton University Press, Princeton, N.J., 1981.       
11 H. Furstenberg and B. Weiss, On almost 1-1 extensions, Israel J. Math., 65 (1989), 311-322.       
12 F. García-Ramos, Weak Forms of Topological and Measure Theoretical Equicontinuity: Relationships with Discrete Spectrum and Sequence Entropy, Ergodic Theory Dynam. Systems, to appear.
13 J. Gillis, Notes on a property of measurable sets, J. London Math. Soc., 11 (1936), 139-141.       
14 E. Glasner, Y. Gutman and X. Ye, Higher order regionally proximal equivalence relations for general group actions, preprint.
15 I. Grigoriev, M. C. Iordan, A. Lubin, N. Ince and C. E. Silva, On $\mu$-compatible metrics and measurable sensitivity, Colloq. Math., 126 (2012), 53-72.       
16 J. Hallett, L. Manuelli and C. E. Silva, On Li-Yorke measurable sensitivity, Proc. Amer. Math. Soc., 143 (2015), 2411-2426.       
17 B. Host, B. Kra and A. Maass, Nilsequences and a structure theory for topological dynamical systems, Adv. Math., 224 (2010), 103-129.       
18 W. Huang, D. Khilko, S. Kolyada and G. H. Zhang, Dynamical compactness and sensitivity, J. Differential Equations, 260 (2016), 6800-6827.       
19 W. Huang, S. Kolyada and G. H. Zhang, Analogues of Auslander-Yorke theorems for multi-sensitivity, Ergodic Theory Dynam. Systems, to appear.
20 W. Huang, P. Lu and X. Ye, Measure-theoretical sensitivity and equicontinuity, Israel J. Math., 183 (2011), 233-283.       
21 W. Huang, S. Shao and X. Ye, Nil Bohr-sets and almost automorphy of higher order, Mem. Amer. Math. Soc., 241 (2016), v+83 pp.       
22 W. Huang and X. Ye, Topological complexity, return times and weak disjointness, Ergodic Theory Dynam. Systems, 24 (2004), 825-846.       
23 J. James, T. Koberda, K. Lindsey, C. E. Silva and P. Speh, Measurable sensitivity, Proc. Amer. Math. Soc., 136 (2008), 3549-3559.       
24 J. Li, Dynamical characterization of C-sets and its application, Fund. Math., 216 (2012), 259-286.       
25 J. Li, Measure-theoretic sensitivity via finite partitions, Nonlinearity, 29 (2016), 2133-2144.       
26 J. Li and X. Ye, Recent development of chaos theory in topological dynamics, Acta Math. Sin. (Engl. Ser.), 32 (2016), 83-114.       
27 R. Li and Y. Shi, Stronger forms of sensitivity for measure-preserving maps and semiflows on probability spaces, Abstr. Appl. Anal., Art., (2014), ID 769523, 10 pages.       
28 H. Liu, L. Liao and L. Wang, Thickly syndetical sensitivity of topological dynamical system, Discrete Dyn. Nat. Soc., Art., (2014), ID 583431, 4 pages.       
29 T. K. S. Moothathu, Stronger forms of sensitivity for dynamical systems, Nonlinearity, 20 (2007), 2115-2126.       
30 D. Ruelle, Dynamical systems with turbulent behavior, Mathematical problems in theoretical physics (Proc. Internat. Conf., Univ. Rome, Rome, 1977), Lecture Notes in Phys., vol. 80, Springer, Berlin-New York, 1978, pp. 341-360.       
31 S. Shao and X. Ye, Regionally proximal relation of order d is an equivalence one for minimal systems and a combinatorial consequence, Adv. Math., 231 (2012), 1786-1817.       
32 H. Wu and H. Wang, Measure-theoretical sensitivity and scrambled sets via Furstenberg families, J. Dyn. Syst. Geom. Theor. 7 (2009), 1-12.       
33 X. Ye and T. Yu, Sensitivity, proximal extension and higher order almost automorphy, Trans. Amer. Math. Soc., 13 (2001).
34 X. Ye and R. Zhang, On sensitive sets in topological dynamics, Nonlinearity, 21 (2008), 1601-1620.       
35 R. Zhang, On sensitivity, Sequence Entropy and Related Problems in Dynamical Systems, Ph.D thesis, University of Science and Technology of China, 2008.

Go to top