Oscillatory integrals and fractal dimension
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