带洞拓扑马尔可夫位移的转移算子的拟紧性

Invariance principle for local time by quasi-compactness

The objective of this paper is to prove a functional weak invariance principle for a local time of a process of the form $X_{n}=φ\circ T^{n}$ where $\left(X,\mathcal{B},T,m\right)$ is a measure preserving system with a transfer operator acting quasi-compactly on a large enough Banach space of functions and $φ\in L^{2}\left(m\right)$ is an aperiodic observable.

半共轭于可数分支分段凸映射的不连续系统的拟紧性与统计性质

Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches

本文研究半共轭于可数分支分段凸映射的不连续斜积系统，证明其转移算子的拟紧性，且存在沿纤维分解为有界变差的不变测度，提出并发展了相关概念。

Quasi-compactness of transfer operators for contact Anosov flows

For any $C^r$ contact Anosov flow with $r\ge 3$, we construct a scale of Hilbert spaces, which are embedded in the space of distributions on the phase space and contain all $C^r$ functions, such that the transfer operators for the flow extend to them boundedly and that the extensions are quasi-compact. Further we give explicit bounds on the essential spectral radii of the extensions in terms of the differentiability r and the hyperbolicity exponents of the flow.

具有可数分支的分段凸映射的 Frobenius-Perron 算子的拟紧性

Quasi-compactness of Frobenius-Perron Operator for Piecewise Convex Maps with Countable Branches

本文利用 Lasota-Yorke 不等式证明了具有可数无穷分支的分段凸映射的 Frobenius-Perron 算子的拟紧性，并确立了其绝对连续不变测度的存在性及系统的强遍历性质。

Compactness of Transfer Operators and Spectral Representation of Ruelle Zeta Functions for Super-continuous Functions

Transfer operators and Ruelle zeta functions for super-continuous functions on one-sided topological Markov shifts are considered. For every super-continuous function, we construct a Banach space on which the associated transfer operator is compact. Using this Banach space, we establish the trace formula and spectral representation of Ruelle zeta functions for a certain class of super-continuous functions. Our results include, as a special case, the classical trace formula and spectral representation for the class of locally constant functions.

On quasi successful couplings of Markov processes

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily Markovian and its components are only converging (in a certain sense) to each other with time. Under these assumptions the unique ergodicity of the original Markov process is proven. A price for this generalization is the weak convergence to the unique invariant measure instead of the strong one. Applying these ideas to infinite interacting particle systems we c…