Finite codimension stability of invariant surfaces
Giovanni Forni
TL;DR
This paper proves finite codimension stability of invariant surfaces in flat geodesic flows on translation surfaces, extending previous work on Hamiltonian systems and para-differential calculus.
Contribution
It introduces a new stability result for invariant surfaces in translation flows, utilizing para-differential calculus and cohomological equations.
Findings
Finite codimension stability established for invariant surfaces.
Applicable to flat geodesic flows on translation surfaces.
Builds on prior work in Hamiltonian systems and cohomological equations.
Abstract
Following recent work of T. Alazard and C. Shao on applications of para-differential calculus to smooth conjugacy and stability problems for Hamiltonian systems, we prove finite codimension stability of invariant surfaces (in finite differentiability classes) of flat geodesic flows on translation surfaces. The result is also based on work of the author on the cohomological equation for translation flows.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Geometry and complex manifolds · Geometric Analysis and Curvature Flows