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8 results

Analysis and Geometry on Graphs and Manifolds
  • Edited by Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski
  • Published online:
    14 August 2020
    Print publication:
    20 August 2020
  • The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.

  • Adding machines and wild attractors

  • HENK BRUIN, GERHARD KELLER, MATTHIAS ST. PIERRE
  • Journal:
    Ergodic Theory and Dynamical Systems / Volume 17 / Issue 6 / December 1997
    Published online by Cambridge University Press:
    01 December 1997, pp. 1267-1287
    Print publication:
    December 1997

  • We investigate the dynamics of unimodal maps $f$ of the interval restrictedto the omega limit set $X$ of the critical point for cases where $X$ is aCantor set.In particular, many cases where $X$ isa measure attractor of $f$ are included. We give two classes of examples ofsuch maps, both generalizing unimodal Fibonacci maps [LM,BKNS]. In allcases $f_{|X}$ is a continuous factor of a generalized odometer (an addingmachine-like dynamical system), and at the same time $f_{|X}$ factors ontoan irrational circle rotation. In some of the examples we obtain irrationalrotations on more complicated groups as factors.