# What is a “stochastic web”?

In this lecture-video (at about 37:17) on Hamiltonian dynamics, the instructor mentions that for an (Arnold-Liouville) integrable finite-dimensional Hamiltonian system one has the following:

• Phase-space dimension: $2N$
• Energy-hypersurface dimension: $2N-1$
• $N$-torus solution-hypersurface dimension: $N$

He then recalls that for $N=2$ and for a given energy (i.e. for a given energy-hypersurface), the dimensionality of the solution-hypersurface (the $N$-torus) is $2$, so for a given solution-hypersurface one can separate the $3$-dimensional energy hypersurface into two parts (inside and outside). He then states that for $N>2$ such a separation isn't possible, because then the difference in dimensionality between a solution-hypersurface and an energy-hypersurface would be greater than $1$. As an example, remember that you can't separate a $3$-dimensional into two parts with a line.

After all this, he says that when $N>2$ the system's phase space becomes a "stochastic web", where solution-hypersurfaces for a given energy cover the corresponding energy in a "web"-like fashion. I would like to know more about this "stochastic web". Where can I find a proper definition of a stochastic web, and also further literature on the topic?

P.S: I didn't know if I should asked this question on MSE.