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#Main properties (classical) 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 ${\frac {1}{2}}$" 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

${\frac {1}{2}}K^{2}n\leq \left\langle {(\Delta p)}^{2}\right\rangle \leq {\frac {1}{2}}K^{2}n^{2}$

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)