There is a necessary and sufficient condition due to Yoccoz in terms of continued fraction expansion. The condition is that $\lambda=e^{2\pi i \theta}$ should be such that $\lambda$ is not a Brjuno number, see

https://en.wikipedia.org/wiki/Brjuno_number

for more details and examples.

There is a necessary and sufficient condition due to Yoccoz in terms of continued fraction expansion. The condition is that $\lambda=e^{2\pi i \theta}$ should be such that $\theta$ is not a Brjuno number, see

https://en.wikipedia.org/wiki/Brjuno_number

for more details and examples.