Talk:Kicked rotator

I humbly think that the Kicked rotator should be a separate topic because it is not a map but a continuous-time model. Only if there is no noise and no disipation it can be reduced to a discrete time map. Otherwise it is essential to keep the time as continuous!

Averaged diffusion of momentum-squared
The section Kicked rotator should specify over which variables and which probability distributions the average $$ \left \langle {(\Delta p)}^{2} \right \rangle$$ is taken.

In particular, the statement "the first term is a sum of $$n$$ terms all equalling $$\frac12$$" in the article holds if the initial conditions modulo $$2\pi$$, i. e. points $$(x(0) \bmod 2\pi,\ p(0) \bmod 2\pi)$$, are uniformly distributed over the square $$[0, 2\pi) \times [0, 2\pi)$$ (because the standard map is area-preserving and thus $$(x(n) \bmod 2\pi,\ p(n) \bmod 2\pi)$$ remains uniformly distributed for any $$n$$) but doesn't hold in case of some other distributions, e. g. if we fix $$p(0) = 0$$ and the average is taken uniformly over $$x(0)$$. Since we are not regarding $$p$$ as periodic, as the introduction says, it is not obvious that we should take $$p(0)$$ uniformly distributed modulo $$2\pi$$. Jaan Vajakas (talk) 15:23, 21 August 2012 (UTC)

It also seems that the conclusion that in the chaotic domain, the momentum diffusion is between
 * $$ \frac{1}{2}K^2n \leq \left \langle {(\Delta p)}^{2} \right \rangle \leq \frac{1}{2}K^2n^2$$

is not rigorous: we considered two limit cases (no correlation and maximal correlation), but why we can conclude that these give us the minimal and maximal bounds? Either a hint of the proof should be given or if there is no proof available then it should be mentioned that this is just an intuitive conclusion, not a rigorously proven formula. Jaan Vajakas (talk) 16:22, 21 August 2012 (UTC)

Хуй
У меня большая проблема с этим вопросом 2A00:1FA0:C4C5:421F:55F5:1B57:10FC:915A (talk) 13:36, 30 November 2021 (UTC)