منابع مشابه
Linearisation of conservative toral homeomorphisms and toral flows
We prove an analogue of Poincaré’s classification of circle homeomorphisms for conservative homeomorphisms of the two-torus with unique rotation vector and a certain bounded mean motion property. In particular, this provides an equivalent characterisation of the semi-conjugacy class of an irrational rotation within the space of conservative toral homeomorphisms. For minimal toral homeomorphisms...
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The familiar Bang/Crunch singularities of classical cosmology have recently been augmented by new varieties: rips, sudden singularities, and so on. These tend to be associated with final states. Here we consider an alternative possibility for the initial state: a singularity which has the novel property of being inaccessible to physically well-defined probes. These singularities arise naturally...
متن کاملLinearisation of conservative toral homeomorphisms
We give an equivalent characterisation of the semi-conjugacy class of an irrational rotation within the space of conservative homeomorphisms of the two-torus. This leads to an analogue of Poincaré’s classification of circle homeomorphisms for conservative toral homeomorphisms with unique rotation vector and a certain bounded mean motion property. For minimal toral homeomorphisms, the result ext...
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This note gives an account of the algebraic construction of symbolic covers and representations of ergodic automorphisms of compact abelian groups. For expansive toral automorphisms this subject was initiated by A.M. Vershik.
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Abstract. We investigate the dimension of the set of points in the d-torus which have the property that their orbit under rotation by some α hits a fixed closed target A more often than expected for all finite initial portions. An upper bound for the lower Minkowski dimension of this strictly heavy set H(A,α) is found in terms of the upper Minkowski dimension of ∂A, as well as k, the Diophantin...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2013
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-013-0470-3