On some nonlinear nonisotropic quasi-self-similar functions

Nonlinear nonisotropic quasi-self-similar functions are important because of their relation with many physical phenomena such as fully developed turbulence or diffusion limited aggregates. Such functions are superpositions of “similar" structures at different scales, reminiscent of some modelization of turbulence. In this paper we continue to study such a class of functions. We extend our results in [Ben Mabrouk. A., Far East J. Dynam. Syst. 7(1), 23–63 (2005)] to some nonlinear cases and where some separation condition is not satisfied. Mathematics subject classification (2000): 42C40, 28A80, 76M55