论文标题
非自治动力系统子集的变异原理：拓扑压力和拓扑熵
Variational principles on subsets of non-autonomous dynamical systems: topological pressure and topological entropy
论文作者
论文摘要
本文讨论了非自治动力学系统拓扑压力和拓扑熵的子集的变异原理。我们为任何子集定义了Pesin-Pitskel拓扑压力（加权拓扑压力）和Bowen拓扑熵（加权Bowen拓扑熵）。此外，我们为所有BOREL概率度量定义了度量理论压力和测量理论下部熵。然后，我们证明了拓扑压力（拓扑熵）的变异原理，该原理将Pesin-Pitskel拓扑压力（加权拓扑压力）与任意的非平台子集与孔孔的理论压力衡量非自治系统（与弓形拓扑的托管型孔托型均与级别的托管型号相关联）非自治动力学系统的Borel概率度量）。 此外，我们表明，可以分别通过度量理论压力和borel概率度量的量度理论下熵来确定Pesin-Pitskel拓扑压力（加权拓扑压力）和Bowen拓扑熵（加权Bowen拓扑熵）。这些结果扩展了冯和黄的结果（子集的拓扑熵的变异原理，J。Fight。Anal。（2012）），MA和WEN的结果（Bowen entropy的Billingsley Type定理，Comptes Rendus Mathematique（2008））和Tang等。结果（对亚集的拓扑压力的变异原理，J。Math。Anal。Appl。（2015））用于非自治动力学系统的压力和熵的经典动力学系统。
This paper discusses the variational principles on subsets for topological pressure and topological entropy of non-autonomous dynamical systems. We define the Pesin-Pitskel topological pressure (weighted topological pressure) and the Bowen topological entropy (weighted Bowen topological entropy) for any subset. Also, we define the measure-theoretic pressure and the measure-theoretic lower entropy for all Borel probability measures. Then, we prove variational principles for topological pressure (topological entropy) which links the Pesin-Pitskel topological pressure (weighted topological pressure) on an arbitrary nonempty compact subset to the measure-theoretic pressure of Borel probability measures for non-autonomous dynamical systems (which links the Bowen topological entropy (weighted Bowen topological entropy) on an arbitrary nonempty compact subset to the measure-theoretic lower entropy of Borel probability measures for non-autonomous dynamical systems). Moreover, we show that the Pesin-Pitskel topological pressure (weighted topological pressure) and the Bowen topological entropy (weighted Bowen topological entropy) can be determined by the measure-theoretic pressure and the measure-theoretic lower entropy of Borel probability measures, respectively. These results extend Feng and Huang's results (Variational principles for topological entropies of subsets, J. Funct. Anal. (2012)), Ma and Wen's results (A Billingsley type theorem for Bowen entropy, Comptes Rendus Mathematique (2008)), and Tang et al. results (Variational principle for topological pressures on subsets, J. Math. Anal. Appl. (2015)) for classical dynamical systems to pressures and entropies of non-autonomous dynamical systems.
