Statistical properties of nonstationary weak Gibbs states and analysis of dissipative phenomena for those invertible extensions

对于非双曲、非可逆的分段可逆系统，在有限值域结构条件下，构造了（bi）非奇异测度和绝对连续不变弱Gibbs测度的自然扩张.进一步，我们得到了判定可逆扩张所产生的过程具有耗散的判据，以及在平衡态附近不存在的、由保持弱Gibbs测度的间歇sofic系统所产生的新现象，即渐近平均熵产生为零的相体积耗散和渐近平均熵产生为零的Gibbs熵的无底源.对于紧度量空间上的部分定义映射族，我们阐明了何时可以确定自同胚集。特别地，在sofic条件下，给出了势函数允许共形测度的一个充分条件。

For nonhyperbolic, noninvertible piecewise invertible systems , we constructed natural extensions of both (bi)nonsingular measures and absolutely continuous invariant weak Gibbs measures under the finite range structure condition. Furthermore, we obtained a criterion for deciding the processes arising from those invertible extensions exhibit dissipation and new phenomena arising from intermittent sofic systems preserving weak Gibbs measures, which are not observed near equilibrium, that is dissipation of the phase volume with zero asymptotic averaged entropy production and bottomless source of the Gibbs entropy with zero asymptotic averaged entropy production. For families of partially defined maps on compact metric spaces, we clarified when self-homeomorphic sets can be determined. In particular, under sofic condition we gave a sufficient condition for potential functions admitting conformal measures.