RigorousInvariantMeasures.jl

A Julia package which implements a implements a flexible scheme to approximate rigorously invariant measures of dynamical systems.

• Library
• • Contractors
  • Preimages
  • Index
• Background
• Abstract basis
• The Ulam basis
• The hat basis on $S^1$
• The hat basis on $[0,1]$
• The C2 basis
• The Chebyshev basis
• Abstract Dynamic Definition
• Piecewise-Map Definition
• Examples
• RigorousInvariantMeasures.jl
• Userguide
• • Building the discretized operator
  • Bounding the norms of the discretized operator
  • Computing the invariant vector and the rigorous error
  • Using the coarse-fine estimates

Citing

If you find useful this package, please cite the paper:

Galatolo S., Nisoli I., An elementary approach to rigorous approximation of invariant measures SIAM J. Appl Dyn Sys.13 pp. 958-985 (2014)

A preprint with a full explanation of the coarse fine scheme is in preparation, by the authors Galatolo S., Monge M., Nisoli I., Poloni F.

License

RigorousInvariantMeasures is licensed under the MIT license; see LICENSE for the full license text.

Installation

RigorousInvariantMeasures.jl is a registered package, and is simply installed by running

pkg> add("RigorousInvariantMeasures")