  We investigate the possibility that the large orbital eccentricity of the
transiting Neptune-mass planet Gliese 436b is maintained in the face of tidal
dissipation by a second planet in the system. We find that the currently
observed configuration can be understood if Gliese 436b and a putative
companion have evolved to a quasi-stationary fixed point in which the planets'
orbital apses are co-linear and in which secular variations in the orbital
eccentricities of the two planets have been almost entirely damped out. We
adopt an octopole-order secular theory based on a Legendre expansion in the
semi-major axis ratio to delineate well-defined regions of (P_c, M_c, e_c)
space that can be occupied by a perturbing companion. We incorporate the
evolutionary effect of tidal dissipation into our secular model of the system,
and solve the resulting initial value problems for a large sample of the
allowed configurations. We then polish the stationary configurations derived
from secular theory with full numerical integrations. We present our results in
the form of candidate companion planets to Gliese 436b. For these candidates,
radial velocity half-amplitudes, K_c, are of order 3 m/s, and the maximum
amplitude of orbit-to-orbit transit timing variations are of order Delta t=1 s
to Delta t=5s. For the particular example case of a perturber with orbital
period, P_c=40 d, mass, M_c=8.5 M_Earth, and eccentricity, e_c=0.58, we confirm
our semi-analytic calculations with a full numerical 3-body integration of the
orbital decay that includes tidal damping and spin evolution. Additionally, we
discuss the possibility of many-perturber stationary configurations, utilizing
modified Laplace-Lagrange secular theory.
