In this paper, we numerically investigate the fraction of nonhyperboli
c parameter values in chaotic dynamical systems. By a nonhyperbolic pa
rameter value we mean a parameter value at which there are tangencies
between some stable and unstable manifolds. The nonhyperbolic paramete
r values are important because the dynamics in such cases is especiall
y pathological. For example, near each such parameter value, there is
another parameter value at which there are infinitely many coexisting
attractors. In particular, Newhouse and Robinson proved that the exist
ence of one nonhyperbolic parameter value typically implies the existe
nce of an interval ('a Newhouse interval') of nonhyperbolic parameter
values. We numerically compute the fraction of nonhyperbolic parameter
values for the Henon map in the parameter range where there exist onl
y chaotic saddles (i.e., nonattracting invariant chaotic sets). We dis
cuss a theoretical model which predicts the fraction of nonhyperbolic
parameter values for small Jacobians. Two-dimensional diffeomorphisms
with similar chaotic saddles may arise in the study of Poincare return
map for physical systems. Our results suggest that (1) nonhyperbolic
chaotic saddles are common in chaotic dynamical systems; and (2) Newho
use intervals can be quite large in the parameter space.