2022/07/03 by Enhui Shi, Hui Xu, Shi, Enhui +1
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Neural Networks Stability and Synchronization #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2207.00979
Let Γ be a higher rank lattice acting on a nondegenerate dendrite X with no infinite order points. We show that there exists a nondegenerate subdendrite Y which is Γ-invariant and satisfies the following items: (1) There is an inverse system of finite actions \(Yi, Γ):i=1,2,3,⋯\ with monotone bonding maps ϕi: Yi+1→ Yi and with each Yi being a dendrite, such that (Y, Γ|Y) is topologically conjugate to the inverse limit (\underset\longleftarrowlim(Yi, Γ), Γ). (2) The first point map r:X→ Y is a factor map from (X, Γ) to (Y, Γ|Y); if x∈ X∖ Y, then r(x) is an end point of Y with infinite orbit; for each y∈ Y, r-1(y) is contractible, that is there is a sequence gi∈ Γ with \rm diam(gir-1(y))→ 0.