arXiv research

Maximal dilatation found on nonorientable surfaces.

The maximal dilatation of certain minimal Lagrangian extensions is bounded by a constant.

The study of which mapping class group elements can be realized as affine automorphisms of dilation surfaces.

We find the minimum dilatation of pseudo-Anosov braids with many strands.

Proposes flexible dilation networks for better time series analysis.

Closed geodesics densely cover a circle in dilation surfaces.

The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example …

This paper describes a family of pseudo-Anosov braids with small dilatation. The smallest dilatations occurring for braids with 3, 4 and 5 strands appear in this family. A pseudo-Anosov braid with 2g+1 strands determines a hyperelliptic mapping class with the same dilatation on a genus-g surface. Penner showed that log…

Minimal dilatations found on nonorientable surfaces with two accumulation points.

Introduces dilation surfaces and their geometric and dynamical aspects.

Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.

In this paper we study the minimum dilatation pseudo-Anosov mapping classes coming from fibrations over the circle of a single 3-manifold, the mapping torus for the "simplest pseudo-Anosov braid". The dilatations that arise include the minimum dilatations for orientable mapping classes for genus g=2,3,4,5,8 as well as …

New formula connects braid dilatation with fixed points.

The paper explores inequalities for strongly-convex sets in weighted Riemannian manifolds.

The paper introduces horizon saddle connections to study dilation surfaces.

Dilated DenseNets excel at relational reasoning without additional modules.

Constructs moduli spaces for complex affine and dilation surfaces.

Based on the notion of dilatation structure arXiv:math/0608536, we give an intrinsic treatment to sub-riemannian geometry, started in the paper arXiv:0706.3644 . Here we prove that regular sub-riemannian manifolds admit dilatation structures. From the existence of normal frames proved by Bellaiche we deduce the rest of…

Study Teichmüller dynamics and dilation tori properties, proving almost all vertical foliations are Morse-Smale.

For a real, non-singular, 2-step nilpotent Lie algebra $\mathfrak{n}$, the group \Aut(\mathfrak{n})/\Aut_0(\mathfrak{n})$, where$\Aut_0(\mathfrak{n})$ is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1-dimensional group of dilations. Maximality of some …

We give upper bounds on the principal curvatures of a maximal surface of nonpositive curvature in three-dimensional Anti-de Sitter space, which only depend on the width of the convex hull of the surface. Moreover, given a quasisymmetric homeomorphism $φ$, we study the relation between the width of the convex hull of th…

We study normed groupoids with dilations and their induced deformations.

Dilated CNN improves multivariate time series classification.

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 surf…

Computes minimal dilatation for Thurston maps on surfaces.

Study on minimal stretching of surface braids with bounds.

This paper concerns a family of pseudo-Anosov braids with dilatations arbitrarily close to one. The associated graph maps and train tracks have stable "star-like" shapes, and the characteristic polynomials of their transition matrices form Salem-Boyd sequences. These examples show that the logarithms of least dilatatio…

The Hopf invariant is linked to null-homotopy properties of maps.

We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…

Paper extends Green-Osher inequality for convex bodies at dilation position.

This note gives a brief survey of the minimum dilatation problem for pseudo-Anosov mapping classes, and the first explicit train track description of an infinite family of pseudo-Anosov mapping classes with orientable stable foliations and the conjectural minimum dilatation for closed surfaces of even genus $g \ge 2$.

Dilated convolutions model long-distance genomic dependencies effectively.

Method detects airway dilatation with high accuracy.

New geometric framework for non-stationary processes using dilation matrices and shape space.

The study improves bounds on pseudo-Anosov maps and certifies minimum and accumulation points of normalized dilatations.

We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained f…

For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner's construction. We also discuss generalisations to surfaces with punctures.

It has been known since 1981 that if one fixes an orientable surface $S$ of genus $g$, then there is a real number $λ_{min,g} > 1$ that is the dilatation of a pA diffeomorphism of $S$, and every other pA diffeomorphism of $S$ has dilatation $\geq λ_{min,g}$. We will show how a little-known theorem about digraphs gives …

We construct homotopically non-trivial maps from S^m to S^n with arbitrarily small 3-dilation for certain pairs (m,n). The simplest example is m=4, n=3. Other examples include arbitrarily large values of m and n. We show that a homotopy class in pi_7(S^4) can be represented by maps with arbitrarily small 4-dilation if …

The paper calculates Veech groups for triangulable structures on the sphere.

It has been known since 1981 that if one fixes an orientable surface $S$ of genus $g$, then there is a real number $λ_{min,g} > 1$ that is the dilatation of a pA diffeomorphism of $S$, and every other pA diffeomorphism of $S$ has dilatation $\geq λ_{min,g}$. We will show how a little-known theorem about digraphs gives …

DILATE improves deep time series forecasting for non-stationary signals.

Constructing transitive nilpotent Lie algebras from dilations and analyzing their prolongations.

The study explores dilating set properties across Euclidean and hyperbolic geometries.

Study Agol cycles on 2-punctured torus and 5-punctured sphere, finding new dilatation formula.

Answering a question of Farb-Leininger-Margalit, we give explicit lower bounds for the dilatations of pseudo-Anosov mapping classes lying in the kth term of the Johnson filtration of the mapping class group.

A filling curve $γ$ on a based surface $S$ determines a pseudo-Anosov homeomorphism $P(γ)$ of $S$ via the process of "point-pushing along $γ$." We consider the relationship between the self-intersection number $i(γ)$ of $γ$ and the dilatation of $P(γ)$; our main result is that the dilatation is bounded between $(i(γ)+1…