Journal: Ergodic Theory and Dynamical Systems

Abbreviation

Ergod. Th. & Dynam. Sys.

Publisher

Cambridge University Press

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ISSN

0143-3857
1469-4417

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Publications 1 - 10 of 28
  • Finitely presented left orderable monsters
    Item type: Journal Article
    Fournier-Facio, Francesco; Lodha, Yash; Zaremsky, Matthew C.B. (2024)
    Ergodic Theory and Dynamical Systems
    A left orderable monster is a finitely generated left orderable group all of whose fixed point-free actions on the line are proximal: the action is semiconjugate to a minimal action so that for every bounded interval I and open interval J, there is a group element that sends I into J. In his 2018 ICM address, Navas asked about the existence of left orderable monsters. By now there are several examples, all of which are finitely generated but not finitely presentable. We provide the first examples of left orderable monsters that are finitely presentable, and even of type F∞. These groups satisfy several additional properties separating them from the previous examples: they are not simple, they act minimally on the circle, and they have an infinite-dimensional space of homogeneous quasimorphisms. Our construction is flexible enough that it produces infinitely many isomorphism classes of finitely presented (and type F∞) left orderable monsters.
  • Homogeneous orbit closures and applications
    Item type: Journal Article
    Lindenstrauss, Elon; Shapira, Uri (2012)
    Ergodic Theory and Dynamical Systems
  • Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on T
    Item type: Journal Article
    Einsiedler, Manfred; Fish, Alexander (2010)
    Ergodic Theory and Dynamical Systems
  • Primitive rational points on expanding horocycles in products of the modular surface with the torus
    Item type: Journal Article
    Einsiedler, Manfred; Luethi, Manuel; Shah, Nimish A. (2021)
    Ergodic Theory and Dynamical Systems
    We prove effective equidistribution of primitive rational points and of primitive rational points defined by monomials along long horocycle orbits in products of the torus and the modular surface. This answers a question posed in joint work by the first and the last named author with Shahar Mozes and Uri Shapira. Under certain congruence conditions we prove the joint equidistribution of conjugate rational points in the -torus and the modular surface.
  • Rigidity properties for commuting automorphisms on tori and solenoids
    Item type: Journal Article
    Einsiedler, Manfred; Lindenstrauss, Elon (2022)
    Ergodic Theory and Dynamical Systems
    Assuming positive entropy, we prove a measure rigidity theorem for higher rank actions on tori and solenoids by commuting automorphisms. We also apply this result to obtain a complete classification of disjointness and measurable factors for these actions.
  • Effectivity of uniqueness of the maximal entropy measure on p-adic homogeneous spaces
    Item type: Journal Article
    Rühr, Rene (2016)
    Ergodic Theory and Dynamical Systems
    We consider the dynamical system given by an Ad-diagonalizable element a of the Qp-points G of a unimodular linear algebraic group acting by translation on a finite volume quotient X. Assuming that this action is exponentially mixing (e.g. if G is simple) we give an effective version (in terms of K-finite vectors of the regular representation) of the following statement: If µ is an a-invariant probability measure with measure theoretical entropy close to the topological entropy of a, then µ is close to the unique G-invariant probability measure of X.
  • Positive Lyapunov exponents for a dense set of bounded measurable SL(2, )-cocycles
    Item type: Journal Article
    Knill, Oliver (1992)
    Ergodic Theory and Dynamical Systems
  • Isospectral sets for boundary value problems on the unit interval
    Item type: Journal Article
    Ralston, James; Trubowitz, Eugene (1988)
    Ergodic Theory and Dynamical Systems
  • Duke's theorem for subcollections
    Item type: Journal Article
    Aka, Menny; Einsiedler, Manfred (2016)
    Ergodic Theory and Dynamical Systems
    We combine effective mixing and Duke’s theorem on closed geodesics on the modular surface to show that certain subcollections of the collection of geodesics with a given discriminant still equidistribute. These subcollections are only assumed to have sufficiently large total length without any further restrictions.
  • A stability theorem for minimal foliations on a torus
    Item type: Journal Article
    Moser, Jürgen (1988)
    Ergodic Theory and Dynamical Systems
Publications 1 - 10 of 28