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Comm. Pure Appl. Math. : A geometric singular perturbation analysis of detonation and deflagration waves. SIAM J. Math. Anal. : Detonation and deflagration waves with multistep reaction schemes. SIAM J. Appl. Math. 55, 175–191 (1995) 50 [HK] [He] [HZ] [HLZ] [HLyZ] [HuZ1] [HuZ2] [JLW] [Kat] [KS] [LS] [LyZ1] [LyZ2] [LRTZ] [MM] [MaZ1] [MaZ2] [MaZ3] [MaZ4] [MaZ5] [MeZ] [Pa] [MT] [RZ] [SS] [ShK] [S1] [S2] [TT] [TZ1] [TZ2] B. Texier, K. : Dynamics and bifurcations. Texts in Applied Mathematics, 3. : Geometric theory of semilinear parabolic equations.

48, 937–992 (1999) Communicated by P. Constantin Commun. Math. Phys. 1007/s00220-010-1177-6 Communications in Mathematical Physics Critical Measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes Polynomials A. Martínez-Finkelshtein1,2 , E. A. Rakhmanov3 1 Department of Statistics and Applied Mathematics, University of Almería, 04120 Almeria, Spain. es 2 Instituto Carlos I de Física Teórica y Computacional, Granada University, 18071 Granada, Spain 3 Department of Mathematics, University of South Florida, Tampa, FL 33620, USA.

Deforming the contour using analyticity of Gλ across oscillatory eigenvalues λ± (ε) we obtain G = G˜ + O, where ε ε O(x, t; y) := eλ+ (ε)t ϕ+ε (x)ϕ˜+ε (y)tr + eλ− (ε)t ϕ− (x)ϕ˜− (y)tr 42 B. Texier, K. Zumbrun ε is the sum of the residues of the integrand at λ± (the right- and left-eigenfunctions ϕ± ε are defined in Sect. 2). The Green function G˜ is the kernel of the integral operand ϕ˜± ator S(ε, t) defined in Sect. 3. 23 applies to G. 21) connecting −ν − iν0 and −ν + iν0 . 8) −ν−iν0 −ν+i∞ 1 GII (ε, x, t; y) := eλt Gλ (ε, x, y) dλ.