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Higher-order variational calculus on Lie algebroids
On the control of stability of periodic orbits of completely integrable systems
1. | The West University of Timişoara, Faculty of Mathematics and C.S., Department of Mathematics, B-dul. Vasile Pârvan, No. 4, 300223 - Timişoara, Romania |
References:
[1] |
P. Birtea, M. Boleanţu, M. Puta and R. M. Tudoran, Asymptotic stability for a class of metriplectic systems, J. Math. Phys., 48 (2007), 082703, 7pp.
doi: 10.1063/1.2771420. |
[2] |
P. Birtea and D. Comănescu, Asymptotic stability of dissipated Hamilton-Poisson systems, SIAM J. Appl. Dyn. Syst., 8 (2009), 967-976.
doi: 10.1137/080735217. |
[3] |
C. Dăniasă, A. Gîrban and R. M. Tudoran, New aspects on the geometry and dynamics of quadratic Hamiltonian systems on $(\mathfrak{so}(3))^{*}$, Int. J. Geom. Methods Mod. Phys., 8 (2011), 1695-1721.
doi: 10.1142/S0219887811005889. |
[4] |
A. Gasull, H. Giacomini and M. Grau, On the stability of periodic orbits for differential systems on $\mathbb{R}^{N}$, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), 495-509.
doi: 10.3934/dcdsb.2008.10.495. |
[5] |
P. Hartman, Ordinary Differential Equations, Classics in Applied Mathematics, 38, SIAM, Philadelphia, 2002.
doi: 10.1137/1.9780898719222. |
[6] |
J. Moser and E. Zehnder, Notes on Dynamical Systems, Courant Lecture Notes in Mathematics, 12, American Mathematical Society, Providence, 2005. |
[7] |
T. S. Ratiu, R. M. Tudoran, L. Sbano, E. Sousa Dias and G. Terra, II: A crash course in geometric mechanics, in Geometric Mechanics and Symmetry (eds. J. Montaldi and T. S. Ratiu), London Mathematical Society Lecture Notes Series, 306, Cambridge University Press, Cambridge, 2005, 23-156.
doi: 10.1017/CBO9780511526367.003. |
[8] |
R. M. Tudoran, Affine Distributions on Riemannian Manifolds with Applications to Dissipative Dynamics, J. Geom. Phys., (2015).
doi: 10.1016/j.geomphys.2015.01.017. |
[9] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, $2^{nd}$ edition, Springer-Verlag, Berlin, 1996.
doi: 10.1007/978-3-642-61453-8. |
show all references
References:
[1] |
P. Birtea, M. Boleanţu, M. Puta and R. M. Tudoran, Asymptotic stability for a class of metriplectic systems, J. Math. Phys., 48 (2007), 082703, 7pp.
doi: 10.1063/1.2771420. |
[2] |
P. Birtea and D. Comănescu, Asymptotic stability of dissipated Hamilton-Poisson systems, SIAM J. Appl. Dyn. Syst., 8 (2009), 967-976.
doi: 10.1137/080735217. |
[3] |
C. Dăniasă, A. Gîrban and R. M. Tudoran, New aspects on the geometry and dynamics of quadratic Hamiltonian systems on $(\mathfrak{so}(3))^{*}$, Int. J. Geom. Methods Mod. Phys., 8 (2011), 1695-1721.
doi: 10.1142/S0219887811005889. |
[4] |
A. Gasull, H. Giacomini and M. Grau, On the stability of periodic orbits for differential systems on $\mathbb{R}^{N}$, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), 495-509.
doi: 10.3934/dcdsb.2008.10.495. |
[5] |
P. Hartman, Ordinary Differential Equations, Classics in Applied Mathematics, 38, SIAM, Philadelphia, 2002.
doi: 10.1137/1.9780898719222. |
[6] |
J. Moser and E. Zehnder, Notes on Dynamical Systems, Courant Lecture Notes in Mathematics, 12, American Mathematical Society, Providence, 2005. |
[7] |
T. S. Ratiu, R. M. Tudoran, L. Sbano, E. Sousa Dias and G. Terra, II: A crash course in geometric mechanics, in Geometric Mechanics and Symmetry (eds. J. Montaldi and T. S. Ratiu), London Mathematical Society Lecture Notes Series, 306, Cambridge University Press, Cambridge, 2005, 23-156.
doi: 10.1017/CBO9780511526367.003. |
[8] |
R. M. Tudoran, Affine Distributions on Riemannian Manifolds with Applications to Dissipative Dynamics, J. Geom. Phys., (2015).
doi: 10.1016/j.geomphys.2015.01.017. |
[9] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, $2^{nd}$ edition, Springer-Verlag, Berlin, 1996.
doi: 10.1007/978-3-642-61453-8. |
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