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Results tagged with ds.dynamical-systems
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user 129192
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
4
votes
1
answer
562
views
Types of triangles admitting periodic billiard orbits
It is an open problem in dynamical systems if every triangle has a periodic billiard orbit. So far it has been proven that equilateral triangles, isosceles triangles, right triangles, and obtuse tria …
- 1,087
0
votes
1
answer
46
views
Conditions required for the orbit of a set of positive measure to cover state space?
Suppose $(X, \mathcal{M}, \mu, T)$ is a measure-preserving dynamical system with $T$ invertible.
I am wondering what properties the dynamical system would need to have in order for the following to be …
- 1,087
33
votes
3
answers
2k
views
Why is the billiard problem for obtuse triangles so hard?
This is an incredibly naive question so this may be closed. Nevertheless, I have been reading about the problem asking if every obtuse triangle admits a periodic billiard path, which has been open fo …
- 1,087
1
vote
0
answers
95
views
Determining the behavior of a contraction mapping with undefined points
Label $X$ as the real interval $[0, a]$ where $a \in \mathbb{R}^+$, so that $\text{int}(X) = (0, a)$ labels the interior of $X$ and $\partial X$ labels the boundary of $X$. I have a function $f:\text …
- 1,087