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Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation
On the dynamics of flows on compact metric spaces
1. | Department of Mathematics, Kyungpook National University, Sankyuk-dong, Buk-gu, Daegu 702-701, South Korea |
2. | Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Gwahak-ro, Yuseong-gu, Daejeon 305-701, South Korea |
[1] |
Carlos Arnoldo Morales, M. J. Pacifico. Lyapunov stability of $\omega$-limit sets. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 671-674. doi: 10.3934/dcds.2002.8.671 |
[2] |
Andrew D. Barwell, Chris Good, Piotr Oprocha, Brian E. Raines. Characterizations of $\omega$-limit sets in topologically hyperbolic systems. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1819-1833. doi: 10.3934/dcds.2013.33.1819 |
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Hongyong Cui, Peter E. Kloeden, Meihua Yang. Forward omega limit sets of nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1103-1114. doi: 10.3934/dcdss.2020065 |
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Bruce Kitchens, Michał Misiurewicz. Omega-limit sets for spiral maps. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 787-798. doi: 10.3934/dcds.2010.27.787 |
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José S. Cánovas. Topological sequence entropy of $\omega$–limit sets of interval maps. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 781-786. doi: 10.3934/dcds.2001.7.781 |
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Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195 |
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Francisco Balibrea, J.L. García Guirao, J.I. Muñoz Casado. A triangular map on $I^{2}$ whose $\omega$-limit sets are all compact intervals of $\{0\}\times I$. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 983-994. doi: 10.3934/dcds.2002.8.983 |
[8] |
Liangwei Wang, Jingxue Yin, Chunhua Jin. $\omega$-limit sets for porous medium equation with initial data in some weighted spaces. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 223-236. doi: 10.3934/dcdsb.2013.18.223 |
[9] |
Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero. Chain recurrence and structure of $ \omega $-limit sets of multivalued semiflows. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2197-2217. doi: 10.3934/cpaa.2020096 |
[10] |
José Ginés Espín Buendía, Víctor Jiménez Lopéz. A topological characterization of the $\omega$-limit sets of analytic vector fields on open subsets of the sphere. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1143-1173. doi: 10.3934/dcdsb.2019010 |
[11] |
Lidong Wang, Hui Wang, Guifeng Huang. Minimal sets and $\omega$-chaos in expansive systems with weak specification property. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1231-1238. doi: 10.3934/dcds.2015.35.1231 |
[12] |
Changjing Zhuge, Xiaojuan Sun, Jinzhi Lei. On positive solutions and the Omega limit set for a class of delay differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (9) : 2487-2503. doi: 10.3934/dcdsb.2013.18.2487 |
[13] |
Wenyu Pan. Effective equidistribution of circles in the limit sets of Kleinian groups. Journal of Modern Dynamics, 2017, 11: 189-217. doi: 10.3934/jmd.2017009 |
[14] |
Jonathan Meddaugh, Brian E. Raines. The structure of limit sets for $\mathbb{Z}^d$ actions. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4765-4780. doi: 10.3934/dcds.2014.34.4765 |
[15] |
Magdalena Foryś-Krawiec, Jana Hantáková, Piotr Oprocha. On the structure of α-limit sets of backward trajectories for graph maps. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1435-1463. doi: 10.3934/dcds.2021159 |
[16] |
Jingxian Sun, Shouchuan Hu. Flow-invariant sets and critical point theory. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 483-496. doi: 10.3934/dcds.2003.9.483 |
[17] |
Ursula Hamenstädt. Dynamics of the Teichmüller flow on compact invariant sets. Journal of Modern Dynamics, 2010, 4 (2) : 393-418. doi: 10.3934/jmd.2010.4.393 |
[18] |
Martin Gugat, Rüdiger Schultz, Michael Schuster. Convexity and starshapedness of feasible sets in stationary flow networks. Networks and Heterogeneous Media, 2020, 15 (2) : 171-195. doi: 10.3934/nhm.2020008 |
[19] |
Qianqian Han, Bo Deng, Xiao-Song Yang. The existence of $ \omega $-limit set for a modified Nosé-Hoover oscillator. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022043 |
[20] |
Krzysztof Barański. Hausdorff dimension of self-affine limit sets with an invariant direction. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1015-1023. doi: 10.3934/dcds.2008.21.1015 |
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