- #1
Sunny Singh
- 19
- 1
I have just started reading chaos from the MIT OpenCourseWare and the following passage has confused me.
"The sensitivity to initial conditions is important to chaos but does not itself differentiate from simple exponential growth, so the aperiodic behavior is also important. In the definition of this somewhat undescriptive phrase we include that the system should undergo Topological Mixing. This means that any points starting in a region (open set) of the phase space will evolve to overlap any other region of the phase space, so chaotic systems tend to explore a larger variety of regions of the phase space"
IF the solution of a system described by linear equations is exponential, then it is aperiodic too right? it won't fall into a periodic orbit for sure. Then how is it not considered to be chaotic? I might be misunderstanding "Topological mixing" here. How does this topological mixing thing leads to such a system not getting called chaotic?
"The sensitivity to initial conditions is important to chaos but does not itself differentiate from simple exponential growth, so the aperiodic behavior is also important. In the definition of this somewhat undescriptive phrase we include that the system should undergo Topological Mixing. This means that any points starting in a region (open set) of the phase space will evolve to overlap any other region of the phase space, so chaotic systems tend to explore a larger variety of regions of the phase space"
IF the solution of a system described by linear equations is exponential, then it is aperiodic too right? it won't fall into a periodic orbit for sure. Then how is it not considered to be chaotic? I might be misunderstanding "Topological mixing" here. How does this topological mixing thing leads to such a system not getting called chaotic?