Please see if the answers and pdfs attached .from another similar q. on RG is useful.

"Swati Khare 12.13

Barrow Neurological Institute

Can anyone share advice on analysis of high speed (slow mo) videos of mice with a tremor?"

  Good luck

Cheers

Additionally enclosed pdf may be of help.

 Cheers

I didn't know what that cat map is, so, thank you for pointing this out.

It seems you can find the period by subjecting the output image of the Arnold function, to the same Arnold function, until your original image reappears. The period depends on the X dimension and possibly also on the Y dimension of the input image; it does not depend on the pixel values.

Thanks, Narasim and Lambert for your help. Yes, periodicity depends on matrix dimension but just want to know is there any method to calculate it directly. Otherwise, I can use loop and run it until we get the same image.

Just a hunch ..approx p where p =periodicity maybe :

  p= n +1 + j*2pi/ log(lambda)    where lambda = min ( negative ) eigen  value of the permutation matrix( ie Arnold matrix) of order n. In the example of n=3 in pdf we get approx p= 5 close to 6.

 Cheers

Hi Narasim,

I appreciate your hunch, but I don't think using 'pi' and a 'log' will lead to an integer number of iterations at which the original image will reappear.

Please see attached pdf .

Cheers