What is the link between chaos and ergodicity in mechanical systems?

[Frank Peters]

There are many formal definitions of an ergodic mechanical system.

1) A system whose time average equals the ensemble (space) average.

2) A system that visits every point in its phase space.

Etc.

What are some actual, real examples of an ergodic mechanical system?

Also, since a chaotic system approaches an attractor and
does not visit all of its phase space, then a chaotic system
is not ergodic. Is this a correct statement?

 

[DrClaude]

The link between chaos and ergodicity is more complicated. Some systems can be both chaotic and ergodic, and some authors call these "strongly chaotic systems" (see Ott, Chaos in Dynamical Systems). Note also that it is dissipative systems that have attractors.

Have a look at: http://biotheory.phys.cwru.edu/phys414/LebowitzPenrose.pdf