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Results tagged with ds.dynamical-systems
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user 25511
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
3
votes
2
answers
286
views
Dynamic of $SL_2(\mathbb{Z}$) on $\mathbb{C}^2$
I imagine the dynamic of $SL(2,\mathbb{Z}$) on $\mathbb{C}^2$ has been studied. Does one know if it is recurrent or ergodic (with respect to the Lebesgue measure) ? Is there any explicit description o …
- 2,696
8
votes
1
answer
766
views
$\omega$-limits of $1$-dimensional dynamical systems
The question that I have in mind is the following:
Which kind of closed sets can arise as the $\omega$-limit of a point for a $1$-dimensional dynamical system?
It is probably somewhat naive, but now …
- 2,696
0
votes
0
answers
74
views
Geodesic flows on affine two-dimensional tori
I am looking for a reference here. Consider a two-dimensional torus $\mathrm{T}^2 =S^1 \times S^1$ together with an affine structure, that is a $(Aff(\mathbb{R}^2), \mathbb{R}^2)$-structure. Such a st …
- 2,696
6
votes
1
answer
606
views
Non uniquely ergodic interval exchange transformations
Consider an interval exchange transformation that is, a bijective piecewise continuous map $[0,1] \rightarrow [0,1] $ whose restriction to its continuity intervals are translations. Assume that it is …
- 2,696
8
votes
4
answers
665
views
Existence of nonergodic polygonal billiard
Let $P$ be a polygon in the plane. One can define the billiard flow on the unit tangent bundle of $P$, just following the trajectories of the billiard at speed one.
A standard conjecture is that a t …
- 2,696
11
votes
2
answers
709
views
Minimal, uniquely ergodic but not Lebesgue-ergodic?
So here's my question:
Does there exist a minimal diffeomorphism of class at least $\mathcal{C^2}$ of a compact manifold X which is
minimal
uniquely ergodic with unique probability measure $\mu$
n …
- 2,696
2
votes
1
answer
319
views
Veech group and mapping class group
So I have this question which is somewhat directed to people knowing a bit about translation surfaces. I am sure it is only a technical issue.
I consider $f : (\Sigma, \omega) \longrightarrow (\Sigma …
- 2,696
13
votes
2
answers
651
views
Closure of the orbits of the $SL(2,\mathbb{Z})$-action on $\mathbb{R}^2$
I'm coming with a very basic question for which I can't find an answer. Please forgive me if I didn't search efficiently enough.
What can the closure of an orbit of an element $X$ of $\mathbb{R}^2$ u …
- 2,696