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Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system
On $ n $-tuplewise IP-sensitivity and thick sensitivity
Department of Mathematics, Shantou University, Shantou, Guangdong, 515063, China |
$ (X,T) $ |
$ n\geq 2 $ |
$ (X,T) $ |
$ n $ |
$ n $ |
$ \delta>0 $ |
$ U $ |
$ X $ |
$ x_1,x_2,\dotsc,x_n\in U $ |
$ \Bigl\{k\in \mathbb{N}\colon \min\limits_{1\le i<j\le n}d(T^k x_i,T^k x_j)>\delta\Bigr\} $ |
$ n $ |
$ n $ |
$ n $ |
$ n\geq 2 $ |
$ n $ |
$ n $ |
$ ^* $ |
$ ^* $ |
$ ^* $ |
References:
[1] |
E. Akin, Recurrence in Topological Dynamics, Furstenberg Families and Ellis Actions, The University Series in Mathematics, Plenum Press, New York, 1997.
doi: 10.1007/978-1-4757-2668-8. |
[2] |
J. Auslander,
On the proximal relation in topological dynamics, Proc. Amer. Math. Soc., 11 (1960), 890-895.
doi: 10.1090/S0002-9939-1960-0164335-7. |
[3] |
J. Auslander, Minimal Flows and Their Extensions, North-Holland Mathematics Studies, 153. Mathematical Notes, 122. North-Holland Publishing Co., Amsterdam, 1988. |
[4] |
J. Auslander and J. A. Yorke,
Interval maps, factors of maps, and chaos, Tohoku Math. J. (2), 32 (1980), 177-188.
doi: 10.2748/tmj/1178229634. |
[5] |
L. Auslander, L. Green and F. Hahn, Flows on Homogeneous Spaces, Annals of Mathematics Studies, 53, Princeton University Press, Princeton, N.J. 1963. |
[6] |
J. Clay,
Variations on equicontinuity, Duke Math. J., 30 (1963), 423-431.
doi: 10.1215/S0012-7094-63-03045-X. |
[7] |
J. P. Clay,
Proximity relations in transformation groups, Trans. Amer. Math. Soc., 108 (1963), 88-96.
doi: 10.1090/S0002-9947-1963-0154269-3. |
[8] |
R. Ellis and W. H. Gottschalk,
Homomorphisms of transformation groups, Trans. Amer. Math. Soc., 94 (1960), 258-271.
doi: 10.1090/S0002-9947-1960-0123635-1. |
[9] |
S. Fomin,
On dynamical systems with a purely point spectrum (in Russian), Dokl. Akad. Nauk SSSR (N.S.), 77 (1951), 29-32.
|
[10] |
H. Furstenberg,
Strict ergodicity and transformation of the torus, Amer. J. Math., 83 (1961), 573-601.
doi: 10.2307/2372899. |
[11] |
H. Furstenberg,
Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Syst. Theory, 1 (1967), 1-49.
doi: 10.1007/BF01692494. |
[12] |
H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, M. B. Porter Lectures, Princeton University Press, Princeton, N.J., 1981. |
[13] |
W. H. He and Z. L. Zhou,
A topologically mixing system whose measure center is a singleton, Acta Math. Sinica (Chin. Ser.), 45 (2002), 929-934.
|
[14] |
W. Huang, S. Kolyada and G. Zhang,
Analogues of Auslander-Yorke theorems for multi-sensitivity, Ergodic Theory Dynam. Systems, 38 (2018), 651-665.
doi: 10.1017/etds.2016.48. |
[15] |
W. Huang, D. Khilko, S. Kolyada, A. Peris and G. Zhang,
Finite intersection property and dynamical compactness, J. Dynam. Differential Equations, 30 (2018), 1221-1245.
doi: 10.1007/s10884-017-9600-8. |
[16] |
J. Li,
Dynamical characterization of C-sets and its application, Fund. Math., 216 (2012), 259-286.
doi: 10.4064/fm216-3-4. |
[17] |
J. Li, S. Tu and X. Ye,
Mean equicontinuity and mean sensitivity, Ergodic Theory Dynam. Systems, 35 (2015), 2587-2612.
doi: 10.1017/etds.2014.41. |
[18] |
J. Li and X. D. Ye,
Recent development of chaos theory in topological dynamics, Acta Math. Sin. (Engl. Ser.), 32 (2016), 83-114.
doi: 10.1007/s10114-015-4574-0. |
[19] |
J. Li and Y. Yang,
Stronger versions of sensitivity for minimal group actions, Acta Math. Sin. (Engl. Ser.), 37 (2021), 1933-1946.
doi: 10.1007/s10114-021-0511-6. |
[20] |
J. Li, X. Ye and T. Yu,
Mean equicontinuity, complexity and applications, Discrete Contin. Dyn. Syst., 41 (2021), 359-393.
doi: 10.3934/dcds.2020167. |
[21] |
T. K. S. Moothathu,
Stronger forms of sensitivity for dynamical systems, Nonlinearity, 20 (2007), 2115-2126.
doi: 10.1088/0951-7715/20/9/006. |
[22] |
F. Tan and R. Zhang,
On $\mathcal{F}$-sensitive pairs, Acta Math. Sci. Ser. B (Engl. Ed.), 31 (2011), 1425-1435.
doi: 10.1016/S0252-9602(11)60328-7. |
[23] |
J. de Vries, Elements of Topological Dynamics, Mathematics and its Applications, 257. Kluwer Academic Publishers Group, Dordrecht, 1993.
doi: 10.1007/978-94-015-8171-4. |
[24] |
J. Xiong,
Chaos in a topologically transitive system, Sci. China Ser. A, 48 (2005), 929-939.
doi: 10.1007/BF02879075. |
[25] |
X. Ye and T. Yu,
Sensitivity, proximal extension and higher order almost automorphy, Trans. Amer. Math. Soc., 370 (2018), 3639-3662.
doi: 10.1090/tran/7100. |
show all references
References:
[1] |
E. Akin, Recurrence in Topological Dynamics, Furstenberg Families and Ellis Actions, The University Series in Mathematics, Plenum Press, New York, 1997.
doi: 10.1007/978-1-4757-2668-8. |
[2] |
J. Auslander,
On the proximal relation in topological dynamics, Proc. Amer. Math. Soc., 11 (1960), 890-895.
doi: 10.1090/S0002-9939-1960-0164335-7. |
[3] |
J. Auslander, Minimal Flows and Their Extensions, North-Holland Mathematics Studies, 153. Mathematical Notes, 122. North-Holland Publishing Co., Amsterdam, 1988. |
[4] |
J. Auslander and J. A. Yorke,
Interval maps, factors of maps, and chaos, Tohoku Math. J. (2), 32 (1980), 177-188.
doi: 10.2748/tmj/1178229634. |
[5] |
L. Auslander, L. Green and F. Hahn, Flows on Homogeneous Spaces, Annals of Mathematics Studies, 53, Princeton University Press, Princeton, N.J. 1963. |
[6] |
J. Clay,
Variations on equicontinuity, Duke Math. J., 30 (1963), 423-431.
doi: 10.1215/S0012-7094-63-03045-X. |
[7] |
J. P. Clay,
Proximity relations in transformation groups, Trans. Amer. Math. Soc., 108 (1963), 88-96.
doi: 10.1090/S0002-9947-1963-0154269-3. |
[8] |
R. Ellis and W. H. Gottschalk,
Homomorphisms of transformation groups, Trans. Amer. Math. Soc., 94 (1960), 258-271.
doi: 10.1090/S0002-9947-1960-0123635-1. |
[9] |
S. Fomin,
On dynamical systems with a purely point spectrum (in Russian), Dokl. Akad. Nauk SSSR (N.S.), 77 (1951), 29-32.
|
[10] |
H. Furstenberg,
Strict ergodicity and transformation of the torus, Amer. J. Math., 83 (1961), 573-601.
doi: 10.2307/2372899. |
[11] |
H. Furstenberg,
Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Syst. Theory, 1 (1967), 1-49.
doi: 10.1007/BF01692494. |
[12] |
H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, M. B. Porter Lectures, Princeton University Press, Princeton, N.J., 1981. |
[13] |
W. H. He and Z. L. Zhou,
A topologically mixing system whose measure center is a singleton, Acta Math. Sinica (Chin. Ser.), 45 (2002), 929-934.
|
[14] |
W. Huang, S. Kolyada and G. Zhang,
Analogues of Auslander-Yorke theorems for multi-sensitivity, Ergodic Theory Dynam. Systems, 38 (2018), 651-665.
doi: 10.1017/etds.2016.48. |
[15] |
W. Huang, D. Khilko, S. Kolyada, A. Peris and G. Zhang,
Finite intersection property and dynamical compactness, J. Dynam. Differential Equations, 30 (2018), 1221-1245.
doi: 10.1007/s10884-017-9600-8. |
[16] |
J. Li,
Dynamical characterization of C-sets and its application, Fund. Math., 216 (2012), 259-286.
doi: 10.4064/fm216-3-4. |
[17] |
J. Li, S. Tu and X. Ye,
Mean equicontinuity and mean sensitivity, Ergodic Theory Dynam. Systems, 35 (2015), 2587-2612.
doi: 10.1017/etds.2014.41. |
[18] |
J. Li and X. D. Ye,
Recent development of chaos theory in topological dynamics, Acta Math. Sin. (Engl. Ser.), 32 (2016), 83-114.
doi: 10.1007/s10114-015-4574-0. |
[19] |
J. Li and Y. Yang,
Stronger versions of sensitivity for minimal group actions, Acta Math. Sin. (Engl. Ser.), 37 (2021), 1933-1946.
doi: 10.1007/s10114-021-0511-6. |
[20] |
J. Li, X. Ye and T. Yu,
Mean equicontinuity, complexity and applications, Discrete Contin. Dyn. Syst., 41 (2021), 359-393.
doi: 10.3934/dcds.2020167. |
[21] |
T. K. S. Moothathu,
Stronger forms of sensitivity for dynamical systems, Nonlinearity, 20 (2007), 2115-2126.
doi: 10.1088/0951-7715/20/9/006. |
[22] |
F. Tan and R. Zhang,
On $\mathcal{F}$-sensitive pairs, Acta Math. Sci. Ser. B (Engl. Ed.), 31 (2011), 1425-1435.
doi: 10.1016/S0252-9602(11)60328-7. |
[23] |
J. de Vries, Elements of Topological Dynamics, Mathematics and its Applications, 257. Kluwer Academic Publishers Group, Dordrecht, 1993.
doi: 10.1007/978-94-015-8171-4. |
[24] |
J. Xiong,
Chaos in a topologically transitive system, Sci. China Ser. A, 48 (2005), 929-939.
doi: 10.1007/BF02879075. |
[25] |
X. Ye and T. Yu,
Sensitivity, proximal extension and higher order almost automorphy, Trans. Amer. Math. Soc., 370 (2018), 3639-3662.
doi: 10.1090/tran/7100. |
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