论文标题
具有奇异性的非符合纤维系统的不变措施
Invariant measures in non-conformal fibered systems with singularities
论文作者
论文摘要
我们研究了一类内态性的不变措施和热力学形式主义$ f_t $，这些$ f_t $仅在数量上可划分的许多零件和非统一形式。内态$ f_t $具有稳定纤维中的参数化生成的限制集。我们证明了$ f_t $的全球音量引理，这意味着平衡度量的投影在非紧凑型全球基本集合$ j_t $上是确切的维度。通过使用Lyapunov指数和边缘熵获得这些全球措施的维度公式。然后，我们研究了几何势的平衡度量，并证明纤维中相关度量的尺寸取决于参数s。此外，我们建立了纤维尺寸的变分原理。
We study invariant measures and thermodynamic formalism for a class of endomorphisms $F_T$ which are only piecewise differentiable on countably many pieces and non-conformal. The endomorphism $F_T$ has parametrized countably generated limit sets in stable fibers. We prove a Global Volume Lemma for $F_T$ implying that the projections of equilibrium measures are exact dimensional on a non-compact global basic set $J_T$. A dimension formula for these global measures is obtained by using the Lyapunov exponents and marginal entropies. Then, we study the equilibrium measures of geometric potentials, and we prove that the dimensions of the associated measures in fibers depend real-analytically on the parameter s. Moreover, we establish a Variational Principle for dimension in fibers.
