2019/06/18 by Guido Ahumada, Ahumada, Guido, Nicolas Chevallier +1
Chemical Engineering · Engineering · Mathematics · #Dynamical Systems (math.DS) #Enhanced Oil Recovery Techniques #FOS: Mathematics #Mathematical Dynamics and Fractals #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1906.07486
openalex publication_date 2019/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an increasing odd homeomorphism σ : R → R, the two bijective maps h σ , v σ : R 2 → R 2 dened by h σ (x, y) = (x + σ --1 (y), y) and v σ (x, y) = (x, σ(x) + y). are called generalized transvections. We study the action on the plane of the group Γ(σ) generated by these two maps. Particularly interesting cases arise when σ(x) = sgn(x)|x| α. We prove that most points have dense orbits and that every nonzero point has a dense orbit when σ(x) = sgn(x)|x| 2. We also look at invariant measures and thanks to Nogueira's work about SL(2, Z)-invariant measure, we can determine these measures when σ is linear in a neighborhood of the origin.