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Polynomial and linearized normal forms for almost periodic differential systems
Supercyclic translation $C_0$-semigroup on complex sectors
1. | School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China |
2. | Department of Mathematics, Tianjin University, Tianjin 300072, China |
References:
[1] |
F. Bayart and E. Matheron, Dynamics of Linear Operators, Camberidge University Press, 2009.
doi: 10.1017/CBO9780511581113. |
[2] |
J. A. Conejero, V. Müller and A. Peris, Hypercyclic behaviour of operators in a hypercyclic $C_0$-semigroup, J. Funct. Anal., 244 (2007), 342-348.
doi: 10.1016/j.jfa.2006.12.008. |
[3] |
J. A. Conejero and A. Peris, Hypercyclic translation $C_0$-semigroups on complex sectors, Discrete Contin. Dyn. Syst., 25 (2009), 1195-1208.
doi: 10.3934/dcds.2009.25.1195. |
[4] |
J. A. Conejero and A. Peris, Chaotic translation semigroups, Discrete Contin. Dyn. Syst. Supplement, (2007), 269-276. |
[5] |
W. Desch, W. Schappacher and G. Webb., Hypercyclic and chaotic semigroup and chaotic semigroup of linear operators, Ergod. Th. Dynam. Sys., 17 (1997), 793-819.
doi: 10.1017/S0143385797084976. |
[6] |
K. G. Grosse-Erdmann and A. P. Manguillot, Linear Chaos, Springer, New York, 2011.
doi: 10.1007/978-1-4471-2170-1. |
[7] |
K. G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math., 139 (2000), 47-68. |
[8] |
G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal., 98 (1991), 229-269.
doi: 10.1016/0022-1236(91)90078-J. |
[9] |
D. A. Herrero, Limits of hypercyclic and supercyclic operators, J. Funct. Anal., 99 (1991), 179-190.
doi: 10.1016/0022-1236(91)90058-D. |
[10] |
Y. X. Liang and Z. H. Zhou, Hereditarily hypercyclicity and supercyclicity of different weighted shifts, J. Korean Math. Soc., 51 (2014), 363-382.
doi: 10.4134/JKMS.2014.51.2.363. |
[11] |
Y. X. Liang and Z. H. Zhou, Hypercyclic behaviour of multiples of composition operators on the weighted Banach space of holomorphic functions, Bull. Belg. Math. Soc. Simon Stevin, 21 (2014), 385-401. |
[12] |
Y. X. Liang and Z. H. Zhou, Supercyclic tuples of the adjoint weighted composition operators on Hilbert spaces, Bull. Iranian Math. Soc., 41 (2015), 121-139. |
[13] |
M. Matsui, M. Yamada and F. Takeo, Supercyclic and chaotic translation semigroups, Proc. Amer. Math. Soc., 131 (2003), 3535-3546.
doi: 10.1090/S0002-9939-03-06960-0. |
[14] |
M. Matsui, M. Yamada and F. Takeo, Erratum to"supercyclic and chaotic translation semigroups", Proc. Amer. Math. Soc., 132 (2004), 3751-3752.
doi: 10.1090/S0002-9939-04-07608-7. |
[15] |
S. Rolewicz, On orbits of elements, Studia Math., 32 (1969), 17-22. |
[16] |
M. Yamada and F. Takeo, Chaotic tranlation semigroups of liear operators, RIMS Koukyroku, 1100 (1999), 8-18. |
[17] |
M. Yamada and F. Takeo, Supercyclic tranlation semigroups of liear operators, RIMS Koukyroku, 1186 (2001), 49-56. |
show all references
References:
[1] |
F. Bayart and E. Matheron, Dynamics of Linear Operators, Camberidge University Press, 2009.
doi: 10.1017/CBO9780511581113. |
[2] |
J. A. Conejero, V. Müller and A. Peris, Hypercyclic behaviour of operators in a hypercyclic $C_0$-semigroup, J. Funct. Anal., 244 (2007), 342-348.
doi: 10.1016/j.jfa.2006.12.008. |
[3] |
J. A. Conejero and A. Peris, Hypercyclic translation $C_0$-semigroups on complex sectors, Discrete Contin. Dyn. Syst., 25 (2009), 1195-1208.
doi: 10.3934/dcds.2009.25.1195. |
[4] |
J. A. Conejero and A. Peris, Chaotic translation semigroups, Discrete Contin. Dyn. Syst. Supplement, (2007), 269-276. |
[5] |
W. Desch, W. Schappacher and G. Webb., Hypercyclic and chaotic semigroup and chaotic semigroup of linear operators, Ergod. Th. Dynam. Sys., 17 (1997), 793-819.
doi: 10.1017/S0143385797084976. |
[6] |
K. G. Grosse-Erdmann and A. P. Manguillot, Linear Chaos, Springer, New York, 2011.
doi: 10.1007/978-1-4471-2170-1. |
[7] |
K. G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math., 139 (2000), 47-68. |
[8] |
G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal., 98 (1991), 229-269.
doi: 10.1016/0022-1236(91)90078-J. |
[9] |
D. A. Herrero, Limits of hypercyclic and supercyclic operators, J. Funct. Anal., 99 (1991), 179-190.
doi: 10.1016/0022-1236(91)90058-D. |
[10] |
Y. X. Liang and Z. H. Zhou, Hereditarily hypercyclicity and supercyclicity of different weighted shifts, J. Korean Math. Soc., 51 (2014), 363-382.
doi: 10.4134/JKMS.2014.51.2.363. |
[11] |
Y. X. Liang and Z. H. Zhou, Hypercyclic behaviour of multiples of composition operators on the weighted Banach space of holomorphic functions, Bull. Belg. Math. Soc. Simon Stevin, 21 (2014), 385-401. |
[12] |
Y. X. Liang and Z. H. Zhou, Supercyclic tuples of the adjoint weighted composition operators on Hilbert spaces, Bull. Iranian Math. Soc., 41 (2015), 121-139. |
[13] |
M. Matsui, M. Yamada and F. Takeo, Supercyclic and chaotic translation semigroups, Proc. Amer. Math. Soc., 131 (2003), 3535-3546.
doi: 10.1090/S0002-9939-03-06960-0. |
[14] |
M. Matsui, M. Yamada and F. Takeo, Erratum to"supercyclic and chaotic translation semigroups", Proc. Amer. Math. Soc., 132 (2004), 3751-3752.
doi: 10.1090/S0002-9939-04-07608-7. |
[15] |
S. Rolewicz, On orbits of elements, Studia Math., 32 (1969), 17-22. |
[16] |
M. Yamada and F. Takeo, Chaotic tranlation semigroups of liear operators, RIMS Koukyroku, 1100 (1999), 8-18. |
[17] |
M. Yamada and F. Takeo, Supercyclic tranlation semigroups of liear operators, RIMS Koukyroku, 1186 (2001), 49-56. |
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