On Peixoto's Conjecture for Flows on Non-orientable 2-Manifolds
Carlos Gutierrez, Benito Pires
Abstract
Let M be a non-orientable compact 2-manifold of genus 4. Then there exists a family of quasi-minimal, Kupka-Smale smooth vector fields Xr in M, depending smoothly on 0<=r<e, such that, for some flow box V in M of X0, and for all 0<=r,v<e, (1) Xr restricted to V is a flow box; (2) If r is not equal to v, Xr is a C∞--twist perturbation of Xv localized in V; (3) Xr and Xv are topologically equivalent.
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