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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 and 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 and Continuous Dynamical Systems  B, 2017, 22 (5) : 19871998. doi: 10.3934/dcdsb.2017117 
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Wenqing Hu, Chris Junchi Li. A convergence analysis of the perturbed compositional gradient flow: Averaging principle and normal deviations. Discrete and 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 and 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 and 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 and 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 and 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 and Continuous Dynamical Systems, 2019, 39 (7) : 40574071. doi: 10.3934/dcds.2019163 
[10] 
Dominic Veconi. SRB measures of singular hyperbolic attractors. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 34153430. doi: 10.3934/dcds.2022020 
[11] 
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 and Continuous Dynamical Systems  B, 2020, 25 (3) : 11411158. doi: 10.3934/dcdsb.2019213 
[12] 
Xiaobin Sun, Jianliang Zhai. Averaging principle for stochastic real GinzburgLandau equation driven by $ \alpha $stable process. Communications on Pure and Applied Analysis, 2020, 19 (3) : 12911319. doi: 10.3934/cpaa.2020063 
[13] 
Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 65816597. doi: 10.3934/dcds.2016085 
[14] 
A. M. López. Finiteness and existence of attractors and repellers on sectional hyperbolic sets. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 337354. doi: 10.3934/dcds.2017014 
[15] 
Aubin Arroyo, Enrique R. Pujals. Dynamical properties of singularhyperbolic attractors. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 6787. doi: 10.3934/dcds.2007.19.67 
[16] 
V. V. Chepyzhov, A. Miranville. Trajectory and global attractors of dissipative hyperbolic equations with memory. Communications on Pure and Applied Analysis, 2005, 4 (1) : 115142. doi: 10.3934/cpaa.2005.4.115 
[17] 
David Parmenter, Mark Pollicott. Gibbs measures for hyperbolic attractors defined by densities. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022038 
[18] 
Peidong Liu, Kening Lu. A note on partially hyperbolic attractors: Entropy conjecture and SRB measures. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 341352. doi: 10.3934/dcds.2015.35.341 
[19] 
Zhicong Liu. SRB attractors with intermingled basins for nonhyperbolic diffeomorphisms. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 15451562. doi: 10.3934/dcds.2013.33.1545 
[20] 
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 
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