Consider an almost periodic trigonometric polynomial $f(t)=e^{i2\pi t} + e^{i 2\pi \lambda t}$ for some irrational $\lambda$. I'm interested in distribution of such polynomial. In other words, is there a Borel measure $\mu$ defined on $X = Cl(f(\mathbb{R}))=2\mathbb{D}$ ($\mathbb{D}$ is the unit disk) such that for every Borel subset $E \subset X$

$$\lim_{T \to +\infty}\frac{1}{T}\int\limits_{0}^{T}\chi_{E}(f(t))dt = \mu(E).$$

The main problem is that we can't define a flow over trajectory due to its self-intersections. So we can't analyze this trajectory via standard dynamical system methods. It is well-known that the line $(t, \lambda t)$ is uniformly distributed on torus $\mathbb{T}^2=\mathbb{R}^2 / \mathbb{Z}^2$ w.r.t. Lebesgue measure. So we may expect the same distribution for $f$.