Tag: Mathematical Dynamics and Fractals
Cohomological equation solved under a periodic-cycle condition
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What the study found For a jointly integrable partially hyperbolic diffeomorphism on a 3-manifold with virtually solvable fundamental group, the cohomological equation has a continuous solution if and only if the function ϕ has trivial periodic cycle functional. Why the authors say this matters The abstract does not state an explicit broader implication or application.…
Recurrence sets have full Hausdorff dimension beyond specification
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in MathematicsWhat the study found The authors introduce a property called (W′)-specification for subshifts, which are symbolic dynamical systems, and show that any recurrence set of a subshift with this property has full Hausdorff dimension. They also report that this applies to a wide class of subshifts without specification, including all S-gap shifts, some coded shifts,…
Hausdorff dimension computed for shrinking targets in affine systems
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in MathematicsWhat the study found The authors compute the Hausdorff dimension of a set of points that recur infinitely often to a shrinking target of geometric balls in certain affine iterated function systems. Their results apply to a representative class of affine systems made of a pair of diagonal affine maps. Why the authors say this…