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Multiscale analysis in Lagrangian formulation for the 2D incompressible Euler equation
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  A, 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  A, 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] 
B. San Martín, Kendry J. Vivas. Asymptotically sectionalhyperbolic attractors. Discrete & Continuous Dynamical Systems  A, 2019, 39 (7) : 40574071. doi: 10.3934/dcds.2019163 
[9] 
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 
[10] 
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 
[11] 
Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete & Continuous Dynamical Systems  A, 2016, 36 (11) : 65816597. doi: 10.3934/dcds.2016085 
[12] 
A. M. López. Finiteness and existence of attractors and repellers on sectional hyperbolic sets. Discrete & Continuous Dynamical Systems  A, 2017, 37 (1) : 337354. doi: 10.3934/dcds.2017014 
[13] 
Aubin Arroyo, Enrique R. Pujals. Dynamical properties of singularhyperbolic attractors. Discrete & Continuous Dynamical Systems  A, 2007, 19 (1) : 6787. doi: 10.3934/dcds.2007.19.67 
[14] 
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 
[15] 
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 
[16] 
Peidong Liu, Kening Lu. A note on partially hyperbolic attractors: Entropy conjecture and SRB measures. Discrete & Continuous Dynamical Systems  A, 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  A, 2013, 33 (4) : 15451562. doi: 10.3934/dcds.2013.33.1545 
[18] 
Huyi Hu, Miaohua Jiang, Yunping Jiang. Infimum of the metric entropy of hyperbolic attractors with respect to the SRB measure. Discrete & Continuous Dynamical Systems  A, 2008, 22 (1&2) : 215234. doi: 10.3934/dcds.2008.22.215 
[19] 
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 
[20] 
Zeng Lian, Peidong Liu, Kening Lu. Existence of SRB measures for a class of partially hyperbolic attractors in banach spaces. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 39053920. doi: 10.3934/dcds.2017164 
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