# Sage Days 112 Online, February-March 2021

Sage is an open source software for mathematics. This is the webpage for the Sage workshop for ANR CODYS. The aim is to:

• introduce Sage to people in the ANR
• implement Loick Lhote's code to compute spectrum of transfer operators on continued fraction algorithms.
• help people to implement their own projects

The workshop will take place on two Thusrday mornings to be determined replacing the weekly sage seminar thursdaysbdx.

## Material

• Daudet-Flajolet-Vallée algorithm on Gauss map notebook.

• Pollicott algorithm for Lyapunov exponents of random matrix products notebook.

## Projects

The following projects have been discussed during the last ANR meeting in December.

• Implement computation of spectra for transfer operators associated to :
1. Gauss map
2. Jacobi-Perron
3. Ostrowski
4. Triangle map
5. ...
• Check Alkauskas theorem.
• Fast approximation of top Lyapunov exponent (Pollicott paper Maximal Lyapunov exponents for random matrix products via periodic orbits and determinant formula)

• See whether it can be extended to simplicial systems... several problems
• use canonical measure instead of Bernoulli measure
• non-negative matrices instead of positive
• Proven enclosure using ball arithmetic and remainder estimates

Here are the project that where mentionned during the first meeting

• "Certify" (or at least check) invariant measures with SageMath [Valerie]

• First Lyapunov exponent using Pollicott https://doi.org/10.1007/s00222-010-0246-y

• Faster algorithm to compute only the k first eigenvalues (instead of the whole spectrum)
• Iterative methods for the computation of the k first eigenvalues and eignfunctions of the spectrum (the (n+1) x (n+1) matrix is obtained from the (n) x (n) matrix by adding one row and one column)... one issue is already to obtain the accuracy at n-th step.
• Higher dimensional Daudet-Flajolet-Vallée (for example Brun in dimension 2, Jacobi-Perron) : Loïck : I can try to apply the method to Brun Algorithm...)

## Support

This workshop is supported by ANR CODYS.

## Other events to (maybe) avoid

Février

• 1 au 5 : JCB

Mars

• 1 au 5 : JNCF
• 15 au 19 : Aléa
• 23 au 26 : Journées nationales du GdR IM

days112 (last edited 2021-03-23 09:09:41 by Fougeroc)