Oscillatory integrals and fractal dimension

Bulletin des Sciences Mathématiques - Tập 168 - Trang 102972 - 2021
Jean-Philippe Rolin1, Domagoj Vlah2, Vesna Županović2
1Université de Bourgogne, Départment de Mathématiques, Institut de Mathématiques de Bourgogne, B.P. 47 870, 21078 Dijon Cedex, France
2University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Applied Mathematics, Unska 3, 10000 Zagreb, Croatia

Tài liệu tham khảo

Arnol'd, 1988, Monodromy and asymptotics of integrals, vol. 83 Tricot, 1995 Žubrinić, 2005, Fractal analysis of spiral trajectories of some planar vector fields, Bull. Sci. Math., 129, 457, 10.1016/j.bulsci.2004.11.007 Žubrinić, 2008, Poincaré map in fractal analysis of spiral trajectories of planar vector fields, Bull. Belg. Math. Soc. Simon Stevin, 15, 947, 10.36045/bbms/1228486418 Mardešić, 2012, Multiplicity of fixed points and growth of ε-neighborhoods of orbits, J. Differ. Equ., 253, 2493, 10.1016/j.jde.2012.06.020 Resman, 2013, Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms, Discrete Contin. Dyn. Syst., 33, 3767, 10.3934/dcds.2013.33.3767 Kostov, 1995, The planar motion with bounded derivative of the curvature and its suboptimal paths, Acta Math. Univ. Comen. (N. S.), 64, 185 Korkut, 2009, Box dimension and Minkowski content of the clothoid, Fractals, 17, 485, 10.1142/S0218348X09004570 Falconer, 1990 Lapidus, 2006, Fractal Geometry, Complex Dimensions and Zeta Functions. Geometry and Spectra of Fractal Strings Županović, 2000, Topological equivalence of planar vector fields and their generalised principal part, J. Differ. Equ., 167, 1, 10.1006/jdeq.2000.3810 Stein, 1993, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, vol. 43 Wong, 2001, Asymptotic Approximations of Integrals, vol. 34 Arnol'd, 1985, The classification of critical points, caustics and wave fronts, vol. 82 Greenblatt, 2009, The asymptotic behavior of degenerate oscillatory integrals in two dimensions, J. Funct. Anal., 257, 1759, 10.1016/j.jfa.2009.06.015 Kamimoto, 2016, Toric resolution of singularities in a certain class of c∞ functions and asymptotic analysis of oscillatory integrals, J. Math. Sci. (Jpn.), 23, 425 Erdélyi, 1956 Korkut, 2016, Wavy spirals and their fractal connection with chirps, Math. Commun., 21, 251 Pašić, 2011, Fractal oscillations of self-adjoint and damped linear differential equations of second-order, Appl. Math. Comput., 218, 2281, 10.1016/j.amc.2011.07.047