A. Milik and P. Szmolyan. Multiple time scales and canards in a chemical oscillator. IMA Preprint 1558, 1998.  Home/Search Document Details and Download
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Theorems of Hartman-Grobman Type for Singularly Perturbed.. - Brunovsky, al. (2002) (Correct)
....description) introduced the technique of blowing up singularities to the study of singularly perturbed systems. These techniques were developed further by Dumortier [9] and Dumortier and Roussarie [11] and as well by Krupa and Szmolyan [27] 28] 29] 30] Szmolyan and other coauthors [36], 42] Fiedler, Liebscher and Alexander [15] and Guckenheimer and Ilyashenko[17] This approach entails the repeated scaling (blowing up) of singularities via polar coordinate transformations until enough hyperbolicity is present so that standard tools of invariant manifold theory can be used. ....
A. Milik and P. Szmolyan, Multiple time scales and canards in a chemical oscillator, in: MultipleTime -Scale Dynamical Systems (Minneapolis, MN,
Viscous profiles for traveling waves of scalar balance laws: The .. - Härterich (1999) (Correct)
....i.e. where the points on C s are hyperbolic with respect to the fast eld. Unfortunately, trajectories that pass near the top of the curve C s are not captured by this classical theory. However, in recent years, methods have been developped by Dumortier and Roussarie [3] and by Milik and Szmolyan [9] to describe those trajectories. 3 Nonexistence of viscous pro les We begin our sequence of proofs with the apparently most complicated heteroclinic waves and show that all discontinuous heteroclinic waves from u i to u i 2 do not admit a viscous pro le. Lemma 3.1 All heteroclinic traveling ....
....large. We do not give the details here since we will not use this estimate later. However, it indicates which might be the correct scaling of s in the blow up construction that is carried out below. 2 4. 2 A Blow up construction The next step is a blow up construction in the spirit of [3] and [6, 7, 9]. In fact, our analysis is close to the one of Krupa and Szmolyan so we only sketch the method and refer to [6] for more details. A similar study in a three dimensional setting is carried out in [9] From the viewpoint of geometrical singular perturbation theory, parts of the singular curve C s ....
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A. Milik and P. Szmolyan. Multiple time scales and canards in a chemical oscillator. IMA Preprint 1558, 1998.
Admissibility of Traveling Waves for Scalar Balance Laws - Härterich (Correct)
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A. Milik and P. Szmolyan. Multiple time scales and canards in a chemical oscillator. IMA Preprint 1558, 1998.
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