Canonical functions of asymptotic diffraction theory associated with symplectic singularities

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1. [1] V. I. Arnol'd, A. N. Varchenko and S. M. Husein-Zade, Singularities of Differentiable Maps, Vol. I, Birkhäuser Verlag, Basel, 1985. 
2. [2] S. Benenti and W. M. Tulczyjew, The Geometrical Meaning and Globalization of the Hamilton-Jacobi Method, in: Differential geometrical methods in mathematical physics, Proc. Conf. Aix-en-Provence/Salamanca 1979, Lecture Notes in Math. 836, Springer, Berlin, 1980, 9-21. 
3. [3] M. G. Brown and F. D. Tappert, Causality, caustics and the structure of transient wavefields, J. Acoust. Soc. Amer. 85 (1986), 251-255. 
4. [4] R. Burridge, The reflection of a pulse in a solid sphere, Proc. Roy. Soc. London A276 (1962), 367-400. Zbl0114.17603
5. [5] J. N. L. Connor, A method for the numerical evaluation of the oscillatory integrals associated with cuspoid catastrophes: applications to Pearcey's integral and its derivatives, J. Phys. A 15 (1982), 1179-1190. Zbl0485.65019
6. [6] J. J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math. 27 (1974), 207-281. Zbl0285.35010
7. [7] M. V. Fedoryuk, Saddle Point Method, Nauka, Moscow, 1977 (in Russian). 
8. [8] M. Golubitsky and V. Guillemin, Stable Mappings and their Singularities, Springer-Verlag, New York, 1973. Zbl0294.58004
9. [9] V. Guillemin and S. Sternberg, Geometric Asymptotics, American Mathematical Society, Providence, RI, 1977. 
10. [10] A. Hanyga, Boundary effects in Asymptotic Diffraction Theory, Part I-III, Seismo-series (int. reports ISEP Univ. of Bergen), Vol. 35-37, Bergen, 1989. 
11. [11] A. Hanyga, Local behaviour of wavefields at simple caustics, Seismo-series (int. reports ISEP Univ. of Bergen), Vol. 38, 1989. 
12. [12] A. Hanyga, Numerical applications of Asymptotic Diffraction Theory, in: Mathematical and Numerical Aspects of Wave Propagation, Univ. of Delaware, June 1993, R. Kleinman et al. (eds.), SIAM, Philadelphia, 1993. Zbl0815.35112
13. [13] A. Hanyga, Asymptotic Diffraction Theory applied to edge-vertex diffraction, in: Proc. 7th Conference on Waves and Stability in Continuous Media, Bologna, Nov. 1993, S. Rionero & T. Ruggeri (eds.), World Scientific Publishing, Singapore, 1994. Zbl0815.35112
14. [14] A. Hanyga, Asymptotic vertex and edge diffraction, Geophys. J. Int. 122 (1995), 277-290. 
15. [15] A. Hanyga and M. Seredyńska, Diffraction of pulses in the vicinity of simple caustics and caustic cusps, Wave Motion 14 (1991), 101-121. Zbl0751.35048
16. [16]S. Janeczko, On isotropic submanifolds and evolution of quasi-caustics, Pacific J. Math. 158 (1993), 317-334. Zbl0806.58023
17. [17] S. Janeczko and G. Plotnikova, Sur la structure de quasi-caustiques en diffraction géometrique, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 543-546. Zbl0714.58019
18. [18] J. B. Keller, Geometrical Theory of Diffraction, J. Opt. Soc. Amer. 52 (1966), 116-130. 
19. [19] Yu. A. Kravtsov and Yu. I. Orlov, Caustics, Catastrophes and Wave Fields, Springer-Verlag, Berlin, 1993. 
20. [20] V. P. Maslov and V. M. Fedoryuk, Semi-classical approximation in quantum mechanics, D. Reidel, Doordrecht, 1981. Zbl0458.58001
21. [21] F. Pham, Singularités des systèmes differentiels de Gauss-Manin, Progr. Math. 2, Birkhäuser, Basel, 1979. Zbl0524.32015
22. [22] T. Poston and I. Stewart, Catastrophe Theory and Its Applications, Pitman, London, 1978. Zbl0382.58006
23. [23] D. Siersma, Singularities of functions on boundaries, corners etc., Quart. J. Math. Oxford (2) 32 (1981), 119-127. Zbl0417.58002
24. [24] D. Stickler, D. S. Ahluwalia and L. Ting, Application of Ludwig's uniform progressing wave ansatz to a smooth caustic, J. Acoust. Soc. Amer. 69 (1981), 1673-1681. Zbl0533.73036
25. [25] A. Weinstein, Lectures on Symplectic Manifolds, in: CBMS Conference Series, American Mathematical Society, Vol. 29, Providence, RI, 1977.