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Attractors for differential equations with multiple variable delays
Observable optimal state points of subadditive potentials
1. | Instituto de Matemática y Estadística Rafael Laguardia, Universidad de la República, Av. Herrera y Reissig 565, C.P.11300, Montevideo, Uruguay |
2. | Department of Mathematics, Soochow University, Suzhou 215006, Jiangsu |
References:
[1] |
Y. Cao, On growth rates of sub-additive functions for semi-flows: determined and random cases, J. Diff. Eqns, 231 (2006), 1-17.
doi: 10.1016/j.jde.2006.08.016. |
[2] |
E. Catsigeras and H. Enrich, SRB-like measures for $C^0$ dynamics, Bull. Polish Acad. Sci. Math., 59 (2011), 151-164.
doi: 10.4064/ba59-2-5. |
[3] |
E. Catsigeras, Milnor-like attractors, preprint, arXiv:1106.4072v2. |
[4] |
X. Dai, Y. Huang and M. Xiao, Periodically switched stability induces exponential stability of discrete-time linear switched systems in the sense of Markovian probabilities, Automatica, 47 (2011), 1512-1519.
doi: 10.1016/j.automatica.2011.02.034. |
[5] |
X. Dai, Optimal state points of the subadditive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573.
doi: 10.1088/0951-7715/24/5/009. |
[6] |
T. Golenishcheva-Kutuzova and V. Kleptsyn, Convergence of the Krylov-Bogolyubov procedure in Bowan's example, (Russian) Mat. Zametki, 82 (2007), 678-689; Translation in Math. Notes, 82 (2007), 608-618. |
[7] |
A. Katok and B. Hasselblatt, "An Introduction to the Modern Theory of Dynamical Systems. Encyclopedia of Mathematics and Its Applications," volume 54, Cambridge: Cambridge University Press, 1995. |
[8] |
J. F. C. Kingman, Subadditive ergodic theory, Ann. Probab., 1 (1973), 883-909. |
[9] |
M. Misiurewicz, Ergodic natural measures, in "Algebraic and Topological Dynamics", volume 385, of Contemp. Math., 1-6 Amer. Math. Soc. Providence R. I. 2005. |
[10] |
S. J. Schreiber, On growth rates of subadditive functions for semi-flows, J. Diff. Eqns, 148 (1998), 334-350.
doi: 10.1006/jdeq.1998.3471. |
[11] |
K. Sigmund, Generic properties of invariant measures for axiom A-diffeomorphisms, Inventiones Math., 11 (1970), 99-109.
doi: 10.1007/BF01404606. |
[12] |
K. Sigmund, On the distribution of periodic points for $\beta-$shifts, Monatsh. Math, 82 (1976), 247-252.
doi: 10.1007/BF01526329. |
[13] |
R. Sturman, and J. Stark, Semi-uniform ergodic theorems and applications to forced systems, Nonlinearity, 13 (2000) 113-143. |
[14] |
Y. Takahashi, Entropy Functional (free energy) for Dynamical Systems and their Random Perturbations, in "Stochastic Analysis North-Holland Math. Library" (Ed. K. It$\hato$), 32 (1982), 437-467. |
[15] |
F. Takens, Heteroclinic attractors: time averages and moduli of topological conjugacy, Bol. Soc. Brasil. Math., 25 (1994), 107-120.
doi: 10.1007/BF01232938. |
[16] |
P. Walters, "An Introduction to Ergodic Theory," GTM 79, New York: Springer, 1982. |
show all references
References:
[1] |
Y. Cao, On growth rates of sub-additive functions for semi-flows: determined and random cases, J. Diff. Eqns, 231 (2006), 1-17.
doi: 10.1016/j.jde.2006.08.016. |
[2] |
E. Catsigeras and H. Enrich, SRB-like measures for $C^0$ dynamics, Bull. Polish Acad. Sci. Math., 59 (2011), 151-164.
doi: 10.4064/ba59-2-5. |
[3] |
E. Catsigeras, Milnor-like attractors, preprint, arXiv:1106.4072v2. |
[4] |
X. Dai, Y. Huang and M. Xiao, Periodically switched stability induces exponential stability of discrete-time linear switched systems in the sense of Markovian probabilities, Automatica, 47 (2011), 1512-1519.
doi: 10.1016/j.automatica.2011.02.034. |
[5] |
X. Dai, Optimal state points of the subadditive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573.
doi: 10.1088/0951-7715/24/5/009. |
[6] |
T. Golenishcheva-Kutuzova and V. Kleptsyn, Convergence of the Krylov-Bogolyubov procedure in Bowan's example, (Russian) Mat. Zametki, 82 (2007), 678-689; Translation in Math. Notes, 82 (2007), 608-618. |
[7] |
A. Katok and B. Hasselblatt, "An Introduction to the Modern Theory of Dynamical Systems. Encyclopedia of Mathematics and Its Applications," volume 54, Cambridge: Cambridge University Press, 1995. |
[8] |
J. F. C. Kingman, Subadditive ergodic theory, Ann. Probab., 1 (1973), 883-909. |
[9] |
M. Misiurewicz, Ergodic natural measures, in "Algebraic and Topological Dynamics", volume 385, of Contemp. Math., 1-6 Amer. Math. Soc. Providence R. I. 2005. |
[10] |
S. J. Schreiber, On growth rates of subadditive functions for semi-flows, J. Diff. Eqns, 148 (1998), 334-350.
doi: 10.1006/jdeq.1998.3471. |
[11] |
K. Sigmund, Generic properties of invariant measures for axiom A-diffeomorphisms, Inventiones Math., 11 (1970), 99-109.
doi: 10.1007/BF01404606. |
[12] |
K. Sigmund, On the distribution of periodic points for $\beta-$shifts, Monatsh. Math, 82 (1976), 247-252.
doi: 10.1007/BF01526329. |
[13] |
R. Sturman, and J. Stark, Semi-uniform ergodic theorems and applications to forced systems, Nonlinearity, 13 (2000) 113-143. |
[14] |
Y. Takahashi, Entropy Functional (free energy) for Dynamical Systems and their Random Perturbations, in "Stochastic Analysis North-Holland Math. Library" (Ed. K. It$\hato$), 32 (1982), 437-467. |
[15] |
F. Takens, Heteroclinic attractors: time averages and moduli of topological conjugacy, Bol. Soc. Brasil. Math., 25 (1994), 107-120.
doi: 10.1007/BF01232938. |
[16] |
P. Walters, "An Introduction to Ergodic Theory," GTM 79, New York: Springer, 1982. |
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