  Let $X$ be a compact connected smooth manifold with boundary. The paper deals
with contact $1$-forms $\beta$ on $X$, whose Reeb vector fields $v_\beta$ admit
Lyapunov functions $f$. We prove that any odd-dimensional $X$ admits such a
contact form.
  We tackle the question: how to recover $X$ and $\beta$ from the appropriate
data along the boundary $\partial X$? We describe such boundary data and prove
that they allow for a reconstruction of the pair $(X, \beta)$, up to a
diffeomorphism of $X$. We use the term ``holography" for the reconstruction. We
say that objects or structures inside $X$ are {\it holographic}, if they can be
reconstructed from their $v_\beta$-flow induced ``shadows" on the boundary
$\partial X$.
  We also introduce numerical invariants that measure how ``wrinkled" the
boundary $\partial X$ is with respect to the $v_\beta$-flow and study their
holographic properties under the contact forms preserving embeddings of
equidimensional contact manifolds with boundary. We get some ``non-squeezing
results" about such contact embedding, which are reminiscent of Gromov's
non-squeezing theorem in symplectic geometry.
