Multiple Canard Cycles in Generalized Liénard Equations

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Geometric singular perturbation analysis of an autocatalator model (2009, methodology): “The blow-up method pioneered by Dumortier and Roussarie [4] has proven to be a powerful tool in the geometric analysis of such problems [2], [5], [6], [10], [12], [13], [14], [15], [21].”
More limit cycles than expected in Liénard equations (2007, background): “As was proved by Dumortier and Roussarie (2005) these bifurcations are controlled by a rational integral computed along the critical curve of the layer equation, called the slow divergence integral.”
Slow Divergence Integral and Balanced Canard Solutions (2011, methodology): “The proof of the results, both in the jump and in the Hopf case, heavily relies on a blow-upofthecontactpoints(see[ 6 ]and[7]).Inthispaperthereisnoneedtorecallthe blow-up technique, since we will only use the properties we stated; the understanding of the property does not require acquaintance with ”