Pierre-Antoine Guihéneuf

Some numerical simulations — page under construction !

Rotation sets for torus homeomorphisms (with Loïc Norgeot).

Some simulations of rotation sets for a one parameter family of torus homeomorphisms:

Fer à cheval

The algorithm used is based on a work of Katja Polotzek, Kathrin Padberg-Gehle and Tobias Jäger, see arXiv:1702.06190. We improve the convergence speed by an algorithm computing the displacement in any direction with a linear complexity.

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Phase portrait of the same family of maps.

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Images of a fundamental domain

Simuations of the images of the fundamental domain [0,1]^2 by a slighly different map, where the sinus is replaces by a piecewise affine map.

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Phase portrait of a family of maps of the annulus

For a two-parameter family of maps of the annulus:

Fer à cheval

composed with a horizontal rotation.

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Discretizations of expanding maps of the circle (with Maurizio Monge)

We compare the ergodic behaviour of uniformly expanding maps of the circle with their spatial discretizations.

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Invariant measures for torus homeomorphisms

Matlab simulations made for the paper Dynamical properties of discretizations of generic homeomorphisms. Here is a user guide for more details (in French, under construction...).

For now these simulations are not very well organized. The files can be downloaded here. Most of the time the file names are quite explicit.

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Periodic points of discretizations of torus homeomorphisms