MODULAR SMOOTHING OF ACTION

The central quantity in the theory of transport for Hamiltonian system s, and in particular the area-preserving twist maps, is the action of rotational periodic orbits. Usually this is a complicated discontinuou s function of two arguments: some perturbation parameter k and a ratio nal rotation number min, denoted by A(k; m/n). We applied the idea of modular smoothing to this complicated fractal. Our main result is that all the information contained in the fractal A(k; m/n) can be retriev ed from a set of continuous or smooth functions of one variable.