A stiction oscillator under slowly varying forcing: Uncovering small scale phenomena using blowup

The paper proves a canard-induced horseshoe for the half-stroboscopic map Rε under (A1)–(A6) by constructing two horizontal strips (from the unstable manifold of a canard) and two vertical stable manifolds, and then verifying Conley–Moser cone conditions to obtain a shift on two symbols. The candidate solution uses the same slow–fast geometry, Fenichel persistence, Exchange Lemma estimates, and invariant cone fields to produce two crossing strips and a Smale horseshoe. Minor divergences include the candidate’s unnecessary claim of a ‘singular horseshoe’ at ε=0 and reliance on a covering property of the singular map R0; the paper avoids these and argues directly at ε>0. Nevertheless, the central mechanism, hypotheses, and estimates align, yielding substantially the same proof structure and conclusion.