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Another proof of the averaging principle for fully coupled dynamical systems with hyperbolic fast motions
1.  Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel 
[1] 
Peng Gao, Yong Li. Averaging principle for the Schrödinger equations^{†}. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 21472168. doi: 10.3934/dcdsb.2017089 
[2] 
Andrej V. Plotnikov, Tatyana A. Komleva, Liliya I. Plotnikova. The averaging of fuzzy hyperbolic differential inclusions. Discrete & Continuous Dynamical Systems  B, 2017, 22 (5) : 19871998. doi: 10.3934/dcdsb.2017117 
[3] 
Wenqing Hu, Chris Junchi Li. A convergence analysis of the perturbed compositional gradient flow: Averaging principle and normal deviations. Discrete & Continuous Dynamical Systems, 2018, 38 (10) : 49514977. doi: 10.3934/dcds.2018216 
[4] 
Jie Xu, Yu Miao, Jicheng Liu. Strong averaging principle for slowfast SPDEs with Poisson random measures. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 22332256. doi: 10.3934/dcdsb.2015.20.2233 
[5] 
Peng Gao. Averaging principle for stochastic KuramotoSivashinsky equation with a fast oscillation. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 56495684. doi: 10.3934/dcds.2018247 
[6] 
Alexander Veretennikov. On large deviations in the averaging principle for SDE's with a "full dependence,'' revisited. Discrete & Continuous Dynamical Systems  B, 2013, 18 (2) : 523549. doi: 10.3934/dcdsb.2013.18.523 
[7] 
Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 11971212. doi: 10.3934/dcdsb.2014.19.1197 
[8] 
David Cheban, Zhenxin Liu. Averaging principle on infinite intervals for stochastic ordinary differential equations. Electronic Research Archive, 2021, 29 (4) : 27912817. doi: 10.3934/era.2021014 
[9] 
B. San Martín, Kendry J. Vivas. Asymptotically sectionalhyperbolic attractors. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 40574071. doi: 10.3934/dcds.2019163 
[10] 
Bin Pei, Yong Xu, Yuzhen Bai. Convergence of pth mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2020, 25 (3) : 11411158. doi: 10.3934/dcdsb.2019213 
[11] 
Xiaobin Sun, Jianliang Zhai. Averaging principle for stochastic real GinzburgLandau equation driven by $ \alpha $stable process. Communications on Pure & Applied Analysis, 2020, 19 (3) : 12911319. doi: 10.3934/cpaa.2020063 
[12] 
Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 65816597. doi: 10.3934/dcds.2016085 
[13] 
A. M. López. Finiteness and existence of attractors and repellers on sectional hyperbolic sets. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 337354. doi: 10.3934/dcds.2017014 
[14] 
Aubin Arroyo, Enrique R. Pujals. Dynamical properties of singularhyperbolic attractors. Discrete & Continuous Dynamical Systems, 2007, 19 (1) : 6787. doi: 10.3934/dcds.2007.19.67 
[15] 
V. V. Chepyzhov, A. Miranville. Trajectory and global attractors of dissipative hyperbolic equations with memory. Communications on Pure & Applied Analysis, 2005, 4 (1) : 115142. doi: 10.3934/cpaa.2005.4.115 
[16] 
Peidong Liu, Kening Lu. A note on partially hyperbolic attractors: Entropy conjecture and SRB measures. Discrete & Continuous Dynamical Systems, 2015, 35 (1) : 341352. doi: 10.3934/dcds.2015.35.341 
[17] 
Zhicong Liu. SRB attractors with intermingled basins for nonhyperbolic diffeomorphisms. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 15451562. doi: 10.3934/dcds.2013.33.1545 
[18] 
Keith Burns, Dmitry Dolgopyat, Yakov Pesin, Mark Pollicott. Stable ergodicity for partially hyperbolic attractors with negative central exponents. Journal of Modern Dynamics, 2008, 2 (1) : 6381. doi: 10.3934/jmd.2008.2.63 
[19] 
Huyi Hu, Miaohua Jiang, Yunping Jiang. Infimum of the metric entropy of hyperbolic attractors with respect to the SRB measure. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 215234. doi: 10.3934/dcds.2008.22.215 
[20] 
Carlos H. Vásquez. Stable ergodicity for partially hyperbolic attractors with positive central Lyapunov exponents. Journal of Modern Dynamics, 2009, 3 (2) : 233251. doi: 10.3934/jmd.2009.3.233 
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