Abstract
We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow us to approximate Sinai-Ruelle-Bowen (SRB)-measures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization of the Frobenius-Perron operator, and two essentially different mathematical concepts are used: our idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from ergodic theory concerning the approximation of SRB-measures by invariant measures of stochastically perturbed systems. The efficiency of the methods is illustrated by several numerical examples.
| Original language | English |
|---|---|
| Pages (from-to) | 491-515 |
| Number of pages | 25 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 36 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1999 |
| Externally published | Yes |
Keywords
- Almost invariant set
- Approximation of the Frobenius-Perron operator
- Computation of SRB-measures
- Computation of invariant measures
- Cyclic behavior