  In this paper we analyze local structure of several chaotic attractors
recently suggested in literature as pseudohyperbolic. The absence of tangencies
and thus the presence of the pseudohyperbolicity is verified using the method
of angles that includes computation of distributions of the angles between the
corresponding tangent subspaces. Also we analyze how volume expansion in the
first subspace and the contraction in the second one occurs locally. For this
purpose we introduce a family of instant Lyapunov exponents. Unlike the well
known finite time ones, the instant Lyapunov exponents show expansion or
contraction on infinitesimal time intervals. Two types of instant Lyapunov
exponents are defined. One is related to ordinary finite time Lyapunov
exponents computed in the course of standard algorithm for Lyapunov exponents.
Their sums reveal instant volume expanding properties. The second type of
instant Lyapunov exponents shows how covariant Lyapunov vectors grow or decay
on infinitesimal time. Using both instant and finite time Lyapunov exponents we
demonstrate that specific to the pseudohyperbolicity average expanding and
contracting properties are typically violated on infinitesimal time. Instantly
volumes from the first subspace can sometimes be contacted, directions in the
second subspace can sometimes be expanded, and the instant contraction in the
first subspace can sometimes be stronger than the contraction in the second
subspace.
