The instability of convection rolls in a fluid layer heatet from below is studied in the case where the layer rotates about an axis slightly inclined with respect to the vertical. The inclination destroys the horizontal isotropy of the layer, but the instability of rolls found by Küppers and Lortz  is little affected as long as the angle of inclination is small. A new effect is the generation of mean Reynolds stresses by rolls not aligned with the horizontal component of the rotation vector. The mean flow exhibits a vorticity of the same sign as the horizontal component of rotation and agrees qualitatively with the mean flow found in the numerical experiments of Hathaway and Somerville 
The origin of a stable spatial pattern in chemical reaction systems has been traced back to symmetries characterized by one-parameter transformation groups. The chemical reaction-diffusion system of Dreitlein and Smoes served as a model for the mathematical approach. The procedure is based on the conversion of sets of partial differential equations to equivalent systems of first order in more parameters. The latter generally admit one-parameter groups, which are related to singularities observed as pattern. It is also shown how models may be constructed from Lie-algebras using the constraints of integrability.
Characteristic functions have been defined in nonlinear autonomous systems. These functions possess properties which are equivalent to those of the energy and the entropy concepts of thermodynamics. The new functions are induced in nonlinear systems by one parameter transformation groups. The mathematical treatment is based on canonical forms and their transformation.
The description of phenomena created by nonlinear oscillators with the aid of transformation groups has been attempted. Such a treatment of the chemical model of Dreitlein and Smoes was met with success. The mathematical approach is based on an application of the canonical form theorem for one-parameter groups. Conditions for the occurence of limit cycles have been derived.