  The transition from quasiperiodicity to chaos is studied in a two-dimensional
dissipative map with the inverse golden mean rotation number. On the basis of a
decimation scheme, it is argued that the (minimal) slope of the critical
iterated circle map is proportional to the effective Jacobian determinant.
Approaching the zero-Jacobian-determinant limit, the factor of proportion
becomes a universal constant. Numerical investigation on the dissipative
standard map suggests that this universal number could become observable in
experiments. The decimation technique introduced in this paper is readily
applicable also to the discrete quasiperiodic Schrodinger equation.
