We study thermodynamical formalism for certain dissipative maps,
that is maps with non-uniformly hyperbolic attractors, which are
obtained from uniformly hyperbolic systems
by the slow down procedure. Namely, starting with a hyperbolic local
diffeomorphism $f : U \to M$ with an attractor $\Lambda$,
one slows down trajectories in a small neighborhood of a hyperbolic fixed
point $p \in \Lambda$ obtaining
a nonuniformly hyperbolic diffeomorphism $g : U \to M$ with a topological
attractor $\Lambda g$. We establish the existence
of equilibrium measures for any continuous potential function on $\Lambda g$,
however our main focus is the family
of geometric $t$-potentials defined by $\varphi t(x) := -t \log|Df|_Eu(x)|$.
We prove
the existence of $t_0 < 0$ such that
the equilibrium measures are unique for every $t \not= 1$ that belongs to
the interval $(t_0,\infty)$. We also identify
equilibrium measures for $t = 1$. Finally, we show that for $t \in (t_0,1)$
the equilibrium measures have
exponential decay of correlations and satisfy the Central Limit Theorem.