-
Previous Article
Periodic and subharmonic solutions for duffing equation with a singularity
- DCDS Home
- This Issue
-
Next Article
Dimensional reduction for supremal functionals
Stable manifolds with optimal regularity for difference equations
1. | Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa |
2. | Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa |
References:
[1] |
L. Barreira and Ya. Pesin, "Nonuniform Hyperbolicity. Dynamics of Systems with Nonzero Lyapunov Exponents," Encyclopedia of Math. and Its Appl., 115, Cambridge Univ. Press, Cambridge, 2007. |
[2] |
L. Barreira and C. Valls, Existence of stable manifolds for nonuniformly hyperbolic $C^1$ dynamics, Discrete Contin. Dyn. Syst., 16 (2006), 307-327.
doi: 10.3934/dcds.2006.16.307. |
[3] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations," Lect. Notes in Math., 1926, Springer, Berlin, 2008. |
[4] |
C. Chicone, "Ordinary Differential Equations with Applications," Second edition, Texts in Applied Mathematics, 34, Springer, New York, 2006. |
[5] |
A. Fathi, M. Herman and J.-C. Yoccoz, A proof of Pesin's stable manifold theorem, in "Geometric Dynamics" (ed. J. Palis, Rio de Janeiro, 1981), Lect. Notes. in Math., 1007, Springer, Berlin, (1983), 177-215. |
[6] |
R. Mañé, Lyapounov exponents and stable manifolds for compact transformations, in "Geometric Dynamics" (ed. J. Palis, Rio de Janeiro, 1981), Lect. Notes in Math., 1007, Springer, Berlin, (1983), 522-577. |
[7] |
V. Oseledec, A multiplicative ergodic theorem. Charactersitc Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179-210. |
[8] |
Ja. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents, Izv. Akad. Nauk SSSR Ser. Mat., 40 (1976), 1332-1379. |
[9] |
Ja. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory, Uspehi Mat. Nauk, 32 (1977), 55-114, 287. |
[10] |
Ja. Pesin, Geodesic flows on closed Riemannian manifolds without focal points, Izv. Akad. Nauk SSSR Ser. Mat., 41 (1977), 1252-1288, 1447. |
[11] |
C. Pugh and M. Shub, Ergodic attractors, Trans. Amer. Math. Soc., 312 (1989), 1-54.
doi: 10.1090/S0002-9947-1989-0983869-1. |
[12] |
D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 27-58. |
[13] |
D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space, Ann. of Math. (2), 115 (1982), 243-290.
doi: 10.2307/1971392. |
show all references
References:
[1] |
L. Barreira and Ya. Pesin, "Nonuniform Hyperbolicity. Dynamics of Systems with Nonzero Lyapunov Exponents," Encyclopedia of Math. and Its Appl., 115, Cambridge Univ. Press, Cambridge, 2007. |
[2] |
L. Barreira and C. Valls, Existence of stable manifolds for nonuniformly hyperbolic $C^1$ dynamics, Discrete Contin. Dyn. Syst., 16 (2006), 307-327.
doi: 10.3934/dcds.2006.16.307. |
[3] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations," Lect. Notes in Math., 1926, Springer, Berlin, 2008. |
[4] |
C. Chicone, "Ordinary Differential Equations with Applications," Second edition, Texts in Applied Mathematics, 34, Springer, New York, 2006. |
[5] |
A. Fathi, M. Herman and J.-C. Yoccoz, A proof of Pesin's stable manifold theorem, in "Geometric Dynamics" (ed. J. Palis, Rio de Janeiro, 1981), Lect. Notes. in Math., 1007, Springer, Berlin, (1983), 177-215. |
[6] |
R. Mañé, Lyapounov exponents and stable manifolds for compact transformations, in "Geometric Dynamics" (ed. J. Palis, Rio de Janeiro, 1981), Lect. Notes in Math., 1007, Springer, Berlin, (1983), 522-577. |
[7] |
V. Oseledec, A multiplicative ergodic theorem. Charactersitc Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179-210. |
[8] |
Ja. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents, Izv. Akad. Nauk SSSR Ser. Mat., 40 (1976), 1332-1379. |
[9] |
Ja. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory, Uspehi Mat. Nauk, 32 (1977), 55-114, 287. |
[10] |
Ja. Pesin, Geodesic flows on closed Riemannian manifolds without focal points, Izv. Akad. Nauk SSSR Ser. Mat., 41 (1977), 1252-1288, 1447. |
[11] |
C. Pugh and M. Shub, Ergodic attractors, Trans. Amer. Math. Soc., 312 (1989), 1-54.
doi: 10.1090/S0002-9947-1989-0983869-1. |
[12] |
D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 27-58. |
[13] |
D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space, Ann. of Math. (2), 115 (1982), 243-290.
doi: 10.2307/1971392. |
[1] |
Redouane Qesmi, Hans-Otto Walther. Center-stable manifolds for differential equations with state-dependent delays. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1009-1033. doi: 10.3934/dcds.2009.23.1009 |
[2] |
Alin Pogan, Kevin Zumbrun. Stable manifolds for a class of singular evolution equations and exponential decay of kinetic shocks. Kinetic and Related Models, 2019, 12 (1) : 1-36. doi: 10.3934/krm.2019001 |
[3] |
Nguyen Thieu Huy, Pham Van Bang. Invariant stable manifolds for partial neutral functional differential equations in admissible spaces on a half-line. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 2993-3011. doi: 10.3934/dcdsb.2015.20.2993 |
[4] |
Carlos Arnoldo Morales. Strong stable manifolds for sectional-hyperbolic sets. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 553-560. doi: 10.3934/dcds.2007.17.553 |
[5] |
Michihiro Hirayama, Naoya Sumi. Hyperbolic measures with transverse intersections of stable and unstable manifolds. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1451-1476. doi: 10.3934/dcds.2013.33.1451 |
[6] |
Mark Pollicott. Ergodicity of stable manifolds for nilpotent extensions of Anosov flows. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 599-604. doi: 10.3934/dcds.2002.8.599 |
[7] |
Luis Barreira, Claudia Valls. Characterization of stable manifolds for nonuniform exponential dichotomies. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1025-1046. doi: 10.3934/dcds.2008.21.1025 |
[8] |
Alexey Gorshkov. Stable invariant manifolds with application to control problems. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021040 |
[9] |
Andrei Fursikov. Local existence theorems with unbounded set of input data and unboundedness of stable invariant manifolds for 3D Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 269-289. doi: 10.3934/dcdss.2010.3.269 |
[10] |
John A. D. Appleby, Xuerong Mao, Alexandra Rodkina. On stochastic stabilization of difference equations. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 843-857. doi: 10.3934/dcds.2006.15.843 |
[11] |
Tao Jiang, Xianming Liu, Jinqiao Duan. Approximation for random stable manifolds under multiplicative correlated noises. Discrete and Continuous Dynamical Systems - B, 2016, 21 (9) : 3163-3174. doi: 10.3934/dcdsb.2016091 |
[12] |
Ale Jan Homburg. Heteroclinic bifurcations of $\Omega$-stable vector fields on 3-manifolds. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 559-580. doi: 10.3934/dcds.1998.4.559 |
[13] |
Zemer Kosloff. On manifolds admitting stable type Ⅲ$_{\textbf1}$ Anosov diffeomorphisms. Journal of Modern Dynamics, 2018, 13: 251-270. doi: 10.3934/jmd.2018020 |
[14] |
Luis Barreira, Claudia Valls. Existence of stable manifolds for nonuniformly hyperbolic $c^1$ dynamics. Discrete and Continuous Dynamical Systems, 2006, 16 (2) : 307-327. doi: 10.3934/dcds.2006.16.307 |
[15] |
Anna Cima, Armengol Gasull, Francesc Mañosas. Global linearization of periodic difference equations. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1575-1595. doi: 10.3934/dcds.2012.32.1575 |
[16] |
Elena Braverman, Alexandra Rodkina. Stochastic difference equations with the Allee effect. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 5929-5949. doi: 10.3934/dcds.2016060 |
[17] |
Eugenia N. Petropoulou. On some difference equations with exponential nonlinearity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2587-2594. doi: 10.3934/dcdsb.2017098 |
[18] |
Ali Akgül, Mustafa Inc, Esra Karatas. Reproducing kernel functions for difference equations. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1055-1064. doi: 10.3934/dcdss.2015.8.1055 |
[19] |
Yazhou Han. Integral equations on compact CR manifolds. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2187-2204. doi: 10.3934/dcds.2020358 |
[20] |
Nguyen Dinh Cong, Thai Son Doan, Stefan Siegmund. On Lyapunov exponents of difference equations with random delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 861-874. doi: 10.3934/dcdsb.2015.20.861 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]