Perturbations of Transfer Operators on Physical Measures, Sampled Recursively on an Orbit
Time: 2022-04-07
Published By: Wenqiong Li
Speaker(s): Angxiu Ni (BICMR)
Time: 14:00-15:00 April 12, 2022
Venue: Room 29, Quan Zhai, BICMR
The physical measure, defined as the weak limit of an orbit, encodes the long-time statistics of a chaotic dynamical system. It is hence interesting to ask if all related quantities (such as perturbations caused by changing parameters) of physical measures can also be sampled recursively on an orbit. This is difficult due to the singularities of measures and the butterfly effect.
For physical measures of hyperbolic dynamical systems, we derive an equivariant divergence formula for the unstable perturbations of transfer operators, which has no exploding intermediate quantities. This formula and the perturbation of physical measures can be sampled by a few recursive relations on one orbit. Some numerical examples are given in higher dimensions.
