Tagged Questions

21 views

Topological conjugacy in Hénon map

$\textbf{Definition:}$ $\textit{(Topologically conjugate)}$ Let $f:A\rightarrow A$ and $g:B\rightarrow B$ be two maps. $f$ and %g% are said to be topologically conjugate if there exists a ...
47 views

Does a pseudo-Anosov homeomorphism of a punctured surface possess infinitely many periodic points?

In A Primer on Mapping Class Groups by Farb and Margalit theorem 14.19 implies that every pseudo-Anosov homeomorphism $f:S \rightarrow S$ on a compact surface $S$ possesses infinitely many periodic ...
44 views

Finite family of subtori in the torus $(S^{1})^{n}$

Working on a problem on matroids, I've already ask a question about some subtori. Here's the link to a previous problem: Topological subspace in $(S^{1})^{n}$ Anyway, here's another problem related ...
420 views

Is the two-dimensional Koch curve space-filling?

Say, we'd like to make a Koch curve with self-similarity dimension of two. A Koch curve with the following generator seems to be two-dimensional, since if we double its size by scaling we'll find ...
102 views

Sketching phase portraits [closed]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
87 views

Is there a general formula for the angles of reflection in a rectangular billiards table?

While writing a program, I encountered a problem in which I needed to calculate the angles of reflection of in a rectangular billiards table. Let's say that we look at the table from above, and that ...
21 views

transversal homoclinic points on a higher-dimensional torus

In many sources (for example introduction to chaotic dynamical systems by Devaney) one can find a proof of the fact that the transversal homoclinic points (points which lay on both stable and unstable ...
82 views

The Starry Rebound

An (infinitely small) ball starting out in the middle of a 5 pointed star table (outer 5 points 10m radius, inner 5 points 5m radius) has a starting angle of a random value from 0 to 360 degrees. The ...
391 views

Proof Strategy for a Dynamical System of Points on the Plane

I have a rather simple-looking system which exhibits a particular behaviour in simulation, and I would now like to attempt to prove this formally. The problem is, I don't really know where to start, ...
153 views

small circle inside embedding of complete graph in the plane

On the web, I found this beautiful drawing of the complete graph on 13 vertices: It is on the Geometry Daily tumblr page. A computer scientist drew a more interactive version up to about 40 ...
71 views

basin of attraction(?) 3d, radius and depth

I'm not so sure I'm using the right terms in this question, but I will try to explain: Say I have a 3d surface, x axis and y are positives, z goes from 0-1. That surface has many "basins"(??), i.e. ...
161 views

Is it possible to capture a light ray in a solar panel?

A while ago I was wondering how we could use mathematics to increase the efficiency of solar panels. The kind of mathematics I was thinking about in particular was Dynamical Billiards. Though I think ...
142 views