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Topological conjugacy of linear systems on Lie groups
1. | Departamento de Matemática, Universidade de Campinas, Campinas, Brazil |
2. | Departamento de Matemática, Universidade Estadual de Maringá, Maringá, Brazil |
3. | Universidade Federal do Paraná, Jandáia do Sul, Brazil |
In this paper we study a classification of linear systems on Lie groups with respect to the conjugacy of the corresponding flows. We also describe stability according to Lyapunov exponents.
References:
[1] |
V. Ayala, F. Colonius and W. Kliemann,
On topological equivalence of linear flows with applications to bilinear control systems, J. Dyn. Control Syst., 13 (2007), 337-362.
doi: 10.1007/s10883-007-9021-9. |
[2] |
F. Colonius and W. Kliemann,
Dynamical Systems and Linear Algebra, American Mathematical Society, 2014. |
[3] |
F. Colonius and A.J. Santana,
Topological conjugacy for affine-linear flows and control systems, Commun. Pure Appl. Anal., 10 (2011), 847-857.
doi: 10.3934/cpaa.2011.10.847. |
[4] |
A. Da Silva,
Controllability of linear systems on solvable Lie groups, SIAM J. Control Optim., 54 (2016), 372-390.
doi: 10.1137/140998342. |
[5] |
C. Kawan, O.G. Rocio and A.J. Santana,
On topological conjugacy of left invariant flows on semisimple and affine Lie groups, Proyecciones, 30 (2011), 175-188.
|
[6] |
N. H. Kuiper and J. W. Robbin,
Topological classification of linear endomorphisms, Invent. Math., 19 (1973), 83-106.
doi: 10.1007/BF01418922. |
[7] |
H. Poincaré,
Sur Les Courbes Definies Par Les Equations Differentielles, In Oeuvres de H. Poincaré I, Gauthier-Villars, Paris, 1928. |
[8] |
J. W. Robbin,
Topological conjugacy and structural stability for discrete dynamical systems, Bull. Amer. Math. Soc., 78 (1972), 923-952.
doi: 10.1090/S0002-9904-1972-13058-1. |
[9] |
C. Robinson,
Dynamical Systems. Stability, Symbolic Dynamics, and Chaos, 2nd Edition, CRC Press, London, 1999. |
show all references
References:
[1] |
V. Ayala, F. Colonius and W. Kliemann,
On topological equivalence of linear flows with applications to bilinear control systems, J. Dyn. Control Syst., 13 (2007), 337-362.
doi: 10.1007/s10883-007-9021-9. |
[2] |
F. Colonius and W. Kliemann,
Dynamical Systems and Linear Algebra, American Mathematical Society, 2014. |
[3] |
F. Colonius and A.J. Santana,
Topological conjugacy for affine-linear flows and control systems, Commun. Pure Appl. Anal., 10 (2011), 847-857.
doi: 10.3934/cpaa.2011.10.847. |
[4] |
A. Da Silva,
Controllability of linear systems on solvable Lie groups, SIAM J. Control Optim., 54 (2016), 372-390.
doi: 10.1137/140998342. |
[5] |
C. Kawan, O.G. Rocio and A.J. Santana,
On topological conjugacy of left invariant flows on semisimple and affine Lie groups, Proyecciones, 30 (2011), 175-188.
|
[6] |
N. H. Kuiper and J. W. Robbin,
Topological classification of linear endomorphisms, Invent. Math., 19 (1973), 83-106.
doi: 10.1007/BF01418922. |
[7] |
H. Poincaré,
Sur Les Courbes Definies Par Les Equations Differentielles, In Oeuvres de H. Poincaré I, Gauthier-Villars, Paris, 1928. |
[8] |
J. W. Robbin,
Topological conjugacy and structural stability for discrete dynamical systems, Bull. Amer. Math. Soc., 78 (1972), 923-952.
doi: 10.1090/S0002-9904-1972-13058-1. |
[9] |
C. Robinson,
Dynamical Systems. Stability, Symbolic Dynamics, and Chaos, 2nd Edition, CRC Press, London, 1999. |
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