Timeline for Strange behavior of $x_{n+1}=x_n +\lambda \sin x_n$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2021 at 7:58 | vote | accept | Vincent Granville | ||
| Jan 30, 2021 at 20:07 | comment | added | Vincent Granville | Note that $\lambda=-8$ yields same behavior as $\lambda=8$. Chaotic behavior of $x_n$ begins when $|\lambda|$ is large enough, around $\lambda=4.60334$ possibly depending on $x_0$ (not that far from the first Feigenbaum constant, in the cases I tested). | |
| Jan 30, 2021 at 18:41 | comment | added | Vincent Granville | The difference with Arnold's tongues seems to be that in my case, $x_n$ should not be interpreted as taken modulo $2\pi$. | |
| Jan 30, 2021 at 17:47 | comment | added | Vincent Granville | Thank you. Short answer, but straight to the point. I will read the literature on this topic. I may add some beautiful pictures obtained when considering the 2-D system $x_{n+1}=x_n +\lambda\sin y_n$, $y_{n+1}=y_n + \lambda \sin x_n$. | |
| Jan 30, 2021 at 12:09 | history | answered | Denis Serre | CC BY-SA 4.0 |