-
Previous Article
A note on almost periodic variational equations
- CPAA Home
- This Issue
-
Next Article
Nonautonomous continuation of bounded solutions
On finite-time hyperbolicity
1. | Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 |
References:
[1] |
A. Berger, T. S. Doan and S. Siegmund, Nonautonomous finite-time dynamics, Discrete Continuous Dynam. Systems - B, 9 (2008), 463-492. |
[2] |
A. Berger, T. S. Doan and S. Siegmund, A remark on finite-time hyperbolicity, PAMM Proc. Appl. Math. Mech., 8 (2008), 10917-10918.
doi: doi:10.1002/pamm.200810917. |
[3] |
A. Berger, T. S. Doan and S. Siegmund, A definition of spectrum for differential equations on finite time, J. Differential Equations, 246 (2009), 1098-1118.
doi: doi:10.1016/j.jde.2008.06.036. |
[4] |
M. Berger and B. Gostiaux, "Differential Geometry: Manifolds, Curves, and Surfaces," Springer, 1988. |
[5] |
A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Mathematics 629, Springer, 1978. |
[6] |
L. H. Duc and S. Siegmund, Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 18 (2008), 641-674.
doi: doi:10.1142/S0218127408020562. |
[7] |
G. Haller, Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos, 10 (2000), 99-108.
doi: doi:10.1063/1.166479. |
[8] |
G. Haller, Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D, 149 (2001), 248-277.
doi: doi:10.1016/S0167-2789(00)00199-8. |
[9] |
G. Haller, Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence, Physics of Fluids, 13 (2001), 3365-3385.
doi: doi:10.1063/1.1403336. |
[10] |
G. Haller, An objective definition of a vortex, J. Fluid Mech., 525 (2005), 1-26.
doi: doi:10.1017/S0022112004002526. |
[11] |
G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147 (2000), 352-370.
doi: doi:10.1016/S0167-2789(00)00142-1. |
[12] |
M. C. Irwin, "Smooth Dynamical Systems," World Scientific, 2001.
doi: doi:10.1142/9789812810120. |
[13] |
T. Kato, "Perturbation Theory for Linear Operators," Springer, 1980. |
[14] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,'' Cambridge University Press, 1995. |
[15] |
K. Palmer, "Shadowing in Dynamical Systems. Theory and Applications," Kluwer, 2000. |
[16] |
R. M. Samelson and S. Wiggins, "Lagrangian Transport in Geophysical Jets and Waves. The Dynamical Systems Approach,'' Springer, 2006. |
[17] |
S. C. Shadden, F. Lekien and J. E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D, 212 (2005), 271-304.
doi: doi:10.1016/j.physd.2005.10.007. |
[18] |
F. Verhulst, "Nonlinear Differential Equations and Dynamical Systems," Springer, 1990. |
show all references
References:
[1] |
A. Berger, T. S. Doan and S. Siegmund, Nonautonomous finite-time dynamics, Discrete Continuous Dynam. Systems - B, 9 (2008), 463-492. |
[2] |
A. Berger, T. S. Doan and S. Siegmund, A remark on finite-time hyperbolicity, PAMM Proc. Appl. Math. Mech., 8 (2008), 10917-10918.
doi: doi:10.1002/pamm.200810917. |
[3] |
A. Berger, T. S. Doan and S. Siegmund, A definition of spectrum for differential equations on finite time, J. Differential Equations, 246 (2009), 1098-1118.
doi: doi:10.1016/j.jde.2008.06.036. |
[4] |
M. Berger and B. Gostiaux, "Differential Geometry: Manifolds, Curves, and Surfaces," Springer, 1988. |
[5] |
A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Mathematics 629, Springer, 1978. |
[6] |
L. H. Duc and S. Siegmund, Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 18 (2008), 641-674.
doi: doi:10.1142/S0218127408020562. |
[7] |
G. Haller, Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos, 10 (2000), 99-108.
doi: doi:10.1063/1.166479. |
[8] |
G. Haller, Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D, 149 (2001), 248-277.
doi: doi:10.1016/S0167-2789(00)00199-8. |
[9] |
G. Haller, Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence, Physics of Fluids, 13 (2001), 3365-3385.
doi: doi:10.1063/1.1403336. |
[10] |
G. Haller, An objective definition of a vortex, J. Fluid Mech., 525 (2005), 1-26.
doi: doi:10.1017/S0022112004002526. |
[11] |
G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147 (2000), 352-370.
doi: doi:10.1016/S0167-2789(00)00142-1. |
[12] |
M. C. Irwin, "Smooth Dynamical Systems," World Scientific, 2001.
doi: doi:10.1142/9789812810120. |
[13] |
T. Kato, "Perturbation Theory for Linear Operators," Springer, 1980. |
[14] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,'' Cambridge University Press, 1995. |
[15] |
K. Palmer, "Shadowing in Dynamical Systems. Theory and Applications," Kluwer, 2000. |
[16] |
R. M. Samelson and S. Wiggins, "Lagrangian Transport in Geophysical Jets and Waves. The Dynamical Systems Approach,'' Springer, 2006. |
[17] |
S. C. Shadden, F. Lekien and J. E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D, 212 (2005), 271-304.
doi: doi:10.1016/j.physd.2005.10.007. |
[18] |
F. Verhulst, "Nonlinear Differential Equations and Dynamical Systems," Springer, 1990. |
[1] |
Arno Berger, Doan Thai Son, Stefan Siegmund. Nonautonomous finite-time dynamics. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 463-492. doi: 10.3934/dcdsb.2008.9.463 |
[2] |
M. Syed Ali, L. Palanisamy, Nallappan Gunasekaran, Ahmed Alsaedi, Bashir Ahmad. Finite-time exponential synchronization of reaction-diffusion delayed complex-dynamical networks. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1465-1477. doi: 10.3934/dcdss.2020395 |
[3] |
Peter Giesl, James McMichen. Determination of the area of exponential attraction in one-dimensional finite-time systems using meshless collocation. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1835-1850. doi: 10.3934/dcdsb.2018094 |
[4] |
Sanjeeva Balasuriya. Uncertainty in finite-time Lyapunov exponent computations. Journal of Computational Dynamics, 2020, 7 (2) : 313-337. doi: 10.3934/jcd.2020013 |
[5] |
Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of a network of strings. Mathematical Control and Related Fields, 2015, 5 (4) : 721-742. doi: 10.3934/mcrf.2015.5.721 |
[6] |
Éder Rítis Aragão Costa. An extension of the concept of exponential dichotomy in Fréchet spaces which is stable under perturbation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 845-868. doi: 10.3934/cpaa.2019041 |
[7] |
Rasul Shafikov, Christian Wolf. Stable sets, hyperbolicity and dimension. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 403-412. doi: 10.3934/dcds.2005.12.403 |
[8] |
Jianjun Paul Tian. Finite-time perturbations of dynamical systems and applications to tumor therapy. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 469-479. doi: 10.3934/dcdsb.2009.12.469 |
[9] |
Shu Dai, Dong Li, Kun Zhao. Finite-time quenching of competing species with constrained boundary evaporation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1275-1290. doi: 10.3934/dcdsb.2013.18.1275 |
[10] |
Grzegorz Karch, Kanako Suzuki, Jacek Zienkiewicz. Finite-time blowup of solutions to some activator-inhibitor systems. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4997-5010. doi: 10.3934/dcds.2016016 |
[11] |
Thierry Cazenave, Yvan Martel, Lifeng Zhao. Finite-time blowup for a Schrödinger equation with nonlinear source term. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1171-1183. doi: 10.3934/dcds.2019050 |
[12] |
Emilija Bernackaitė, Jonas Šiaulys. The finite-time ruin probability for an inhomogeneous renewal risk model. Journal of Industrial and Management Optimization, 2017, 13 (1) : 207-222. doi: 10.3934/jimo.2016012 |
[13] |
Tingting Su, Xinsong Yang. Finite-time synchronization of competitive neural networks with mixed delays. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3655-3667. doi: 10.3934/dcdsb.2016115 |
[14] |
Tianhu Yu, Jinde Cao, Chuangxia Huang. Finite-time cluster synchronization of coupled dynamical systems with impulsive effects. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3595-3620. doi: 10.3934/dcdsb.2020248 |
[15] |
Khalid Addi, Samir Adly, Hassan Saoud. Finite-time Lyapunov stability analysis of evolution variational inequalities. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1023-1038. doi: 10.3934/dcds.2011.31.1023 |
[16] |
Peter Giesl. Construction of a finite-time Lyapunov function by meshless collocation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2387-2412. doi: 10.3934/dcdsb.2012.17.2387 |
[17] |
Gang Tian. Finite-time singularity of Kähler-Ricci flow. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1137-1150. doi: 10.3934/dcds.2010.28.1137 |
[18] |
E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics and Games, 2018, 5 (2) : 165-185. doi: 10.3934/jdg.2018010 |
[19] |
Alfonso C. Casal, Jesús Ildefonso Díaz, José M. Vegas. Finite extinction time property for a delayed linear problem on a manifold without boundary. Conference Publications, 2011, 2011 (Special) : 265-271. doi: 10.3934/proc.2011.2011.265 |
[20] |
Huijuan Li, Junxia Wang. Input-to-state stability of continuous-time systems via finite-time Lyapunov functions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 841-857. doi: 10.3934/dcdsb.2019192 |
2021 Impact Factor: 1.273
Tools
Metrics
Other articles
by authors
[Back to Top]