A Piecewise Smooth λ-Lemma

2025/07/15 by Buzzi, Claudio A., Santana, Paulo, Silva, Luan V. M. F.
#34A36 #37C29 #Dynamical Systems (math.DS) #FOS: Mathematics #and 34C37

paper · doi:10.48550/arxiv.2507.10896

Abstract

In this paper we provide extensions of the λ-Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth vector fields defined at crossing orbits. We prove that these maps are homeomorphisms and also piecewise smooth diffeomorphisms.

Citations

• The Orbit Space Approach for Piecewise Smooth Vector Fields
• Slow--fast systems and sliding on codimension 2 switching manifolds
• The Melnikov method and subharmonic orbits in a piecewise smooth system
• Generic bifurcations of low codimension of planar Filippov Systems

Related

• The Orbit Space Approach for Piecewise Smooth Vector Fields
• Equivariant smoothing of piecewise linear manifolds
• Non-smoothability for a class of groups of piecewise linear homeomorphisms of the interval
• Consecutive shifts along orbits of vector fields
• A piecewise-linear fixed point theorem