# American Institute of Mathematical Sciences

eISSN:
2688-1594

All Issues

## Electronic Research Archive

### Special issue on stability and complexity of differential systems

David Cheban, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China; State University of Moldova, Faculty of Mathematics and Informatics, Department of Mathematics, A. Mateevich Street 60, MD--2009 Chişinău, Moldova cheban@usm.md
Wen Huang, CAS Wu Wen-Tsun Key Laboratory of Mathematics, and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China wenh@mail.ustc.edu.cn
Zhenxin Liu, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China zxliu@dlut.edu.cn

2021, 29(4): 2791-2817 doi: 10.3934/era.2021014 +[Abstract](349)+[HTML](157) +[PDF](410.94KB)
Abstract:

In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations in Hilbert space with Poisson stable (in particular, periodic, quasi-periodic, almost periodic, almost automorphic etc) coefficients. Under some appropriate conditions we prove that there exists a unique recurrent solution to the original equation, which possesses the same recurrence property as the coefficients, in a small neighborhood of the stationary solution to the averaged equation, and this recurrent solution converges to the stationary solution of averaged equation uniformly on the whole real axis when the time scale approaches zero.

2021, 29(4): 2819-2827 doi: 10.3934/era.2021015 +[Abstract](299)+[HTML](167) +[PDF](330.89KB)
Abstract:

In this paper we study ergodic measures of intermediate entropy for affine transformations of nilmanifolds. We prove that if an affine transformation \begin{document}$\tau$\end{document} of nilmanifold has a periodic point, then for every \begin{document}$a\in[0, h_{top}(\tau)]$\end{document} there exists an ergodic measure \begin{document}$\mu_a$\end{document} of \begin{document}$\tau$\end{document} such that \begin{document}$h_{\mu_a}(\tau) = a$\end{document}.

2021, 29(5): 3069-3079 doi: 10.3934/era.2021026 +[Abstract](15)+[HTML](11) +[PDF](807.77KB)
Abstract:
2021, 29(5): 3081-3096 doi: 10.3934/era.2021027 +[Abstract](15)+[HTML](11) +[PDF](525.34KB)
Abstract:
2021, 29(6): 4177-4198 doi: 10.3934/era.2021078 +[Abstract](15)+[HTML](11) +[PDF](642.28KB)
Abstract:

2020 Impact Factor: 1.833
5 Year Impact Factor: 1.833