Timeline for Is it possible for a system to be chaotic but not ergodic? If so, how?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 29, 2021 at 20:13 | comment | added | stafusa | @ComptonScattering No, sorry, not out of the top of my head. | |
| Dec 29, 2021 at 15:44 | comment | added | ComptonScattering | Do you know if there are examples for which every invariant manifold is individually chaotic, but the system is not ergodic? (I guess with some kind of additional stability criteria to rule out tensor product cases like the following: let $f : [0,1) \to [0,1)$ define a chaotic map, let consider $g : [0,2) \to [0,2)$ defined by $g(x) = f(x)$ for $x \in [0,1)$ and $g(x) = f(x-1)+1$ for $x \in [1,2)$. $g$ is not ergodic due to the conservation law $\lfloor x \rfloor = \lfloor g(x) \rfloor$) | |
| Dec 29, 2021 at 10:56 | comment | added | stafusa | @ComptonScattering Yes, it's very usual, especially in physics. If a system can exhibit chaos, you can call it chaotic, as is done, e.g., with the double pendulum. | |
| Dec 29, 2021 at 6:44 | comment | added | ComptonScattering | Is it usual to refer to a system as chaotic if there or invariant measures on which the maximal Lyapunov exponent is not positive? I though Lyapunov exponents (and hence chaoticity) are properties of an invariant measure, rather than the dynamical system. | |
| Mar 6, 2021 at 13:27 | vote | accept | Emilio Pisanty | ||
| May 12, 2019 at 21:23 | history | answered | stafusa | CC BY-SA 4.0 |