Displaying similar documents to “A note on pseudo-Anosov maps with small growth rate.”

On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus

Erwan Lanneau, Jean-Luc Thiffeault (2011)

Annales de l’institut Fourier

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We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus g = 2 to 5 , the minimum dilatation is the smallest Salem number for polynomials of degree 2 g .

Embedding tiling spaces in surfaces

Charles Holton, Brian F. Martensen (2008)

Fundamenta Mathematicae

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We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface...

Approximate roots of pseudo-Anosov diffeomorphisms

T. M. Gendron (2009)

Annales de l’institut Fourier

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The Root Conjecture predicts that every pseudo-Anosov diffeomorphism of a closed surface has Teichmüller approximate n th roots for all n 2 . In this paper, we replace the Teichmüller topology by the heights-widths topology – that is induced by convergence of tangent quadratic differentials with respect to both the heights and widths functionals – and show that every pseudo-Anosov diffeomorphism of a closed surface has heights-widths approximate n th roots for all n 2 .

Rotation surfaces with L₁-pointwise 1-type Gauss map in pseudo-Galilean space

Dae Won Yoon, Young Ho Kim, Jae Seong Jung (2015)

Annales Polonici Mathematici

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We study rotation surfaces in the three-dimensional pseudo-Galilean space G₃¹ such that the Gauss map G satisfies the condition L₁G = f(G + C) for a smooth function f and a constant vector C, where L₁ is the Cheng-Yau operator.

Identifying points of a pseudo-Anosov homeomorphism

Gavin Band (2003)

Fundamenta Mathematicae

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We investigate the question, due to S. Smale, of whether a hyperbolic automorphism T of the n-dimensional torus can have a compact invariant subset homeomorphic to a compact manifold of positive dimension, other than a finite union of subtori. In the simplest case such a manifold would be a closed surface. A result of Fathi says that T can sometimes have an invariant subset which is a finite-to-one image of a closed surface under a continuous map which is locally injective except possibly...

On pseudo-isotopy classes of homeomorphisms of a dimensional differentiable manifold.

Alberto Cavicchioli, Friedrich Hegenbarth (1998)

Revista Matemática Complutense

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We study self-homotopy equivalences and diffeomorphisms of the (n+1)-dimensional manifold X= #p(S1 x Sn) for any n ≥ 3. Then we completely determine the group of pseudo-isotopy classes of homeomorphisms of X and extend to dimension n well-known theorems due to F. Laudenbach and V. Poenaru (1972,1973), and J. M. Montesinos (1979).

Shadowing and expansivity in subspaces

Andrew D. Barwell, Chris Good, Piotr Oprocha (2012)

Fundamenta Mathematicae

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We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.