10 citations · 12 across the 7 of their papers we have counts for
11 papers
Thin Gordian Unlinks
José Ayala
A gordian unlink is a finite number of unknots that are not topologically linked, each with prescribed length and thickness, and that cannot be disentangled into the trivial link b…
A Gradient Descent Method for The Dubins Traveling Salesman Problem
David Kirszenblat, José Ayala, J. Hyam Rubinstein
We propose a combination of a bounding procedure and gradient descent method for solving the Dubins traveling salesman problem, that is, the problem of finding a shortest curvature…
On the Blaschke rolling disk theorem
José Ayala
The Blaschke rolling disk theorem is a classical inclusion principle in differential geometry. This states that a planar convex domain whose boundary is a curve of class with…
Census of bounded curvature paths
Jean Díaz, José Ayala
A bounded curvature path is a continuously differentiable piece-wise path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These path…
Immersed flat ribbon knots
José Ayala, David Kirszenblat, J. Hyam Rubinstein
We study the minimum ribbonlength for immersed planar ribbon knots and links. Our approach is to embed the space of such knots and links into a larger more tractable space of disk…
Topological dynamics on finite directed graphs
José Ayala, Wolfgang Kliemann
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed g…
On the topology of the spaces of curvature constrained plane curves
José Ayala
It is well known that plane curves with the same endpoints are homotopic. An analogous claim for plane curves with the same endpoints and bounded curvature still remains open. In t…
The classification of homotopy classes of bounded curvature paths
José Ayala, J. Hyam Rubinstein
A bounded curvature path is a continuously differentiable piecewise path with bounded absolute curvature that connects two points in the tangent bundle of a surface. In this…
Length minimising bounded curvature paths in homotopy classes
José Ayala
Choose two points in the tangent bundle of the Euclidean plane . In this work we characterise the immersed length minimising paths with a prescribed…
Non-uniqueness of the homotopy class of bounded curvature paths
José Ayala, Hyam Rubinstein
A bounded curvature path is a continuously differentiable piecewise path with a bounded absolute curvature that connects two points in the tangent bundle of a surface. In thi…
A geometric approach to shortest bounded curvature paths
José Ayala, David Kirszenblat, J. Hyam Rubinstein
Consider two elements in the tangent bundle of the Euclidean plane . In this work we address the problem of characterizing the paths of bounded curva…