Abstract We construct axisymmetric self-similar solutions of transonic outflows emanating from a point source including the effect rotation. The are constructed exclusively on equatorial plane. features determined by three parameters: adiabatic index γ , dimensionless coordinate point, and azimuthal velocity at point. classify into five groups according to asymptotic behaviors. find that behavi...

We present results of a numerical renormalization approximation to the self-similar growth of clustering of a collisionless pressureless fluid out of a power-law spectrum of primeval Gaussian mass density fluctuations, P (k) ∝ kn, in an Einstein-de Sitter cosmological model. The self-similar position two-point correlation function, ξ(r), seems to be well established. The renormalization solutio...

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...