  Recent observations show that our universe is accelerating by dark energy, so
it is important to investigate the thermodynamical properties of it. The
Undulant
  Universe is a model with equation of state $\omega(a)=-\cos(b\ln a)$ for dark
energy, where we show that there neither the event horizon nor the particle
horizon exists. However, as a boundary of keeping thermodynamical properties,
the apparent horizon is a good holographic screen. The Universe has a thermal
equilibrium inside the apparent horizon, so the Unified First Law and the
Generalized Second Law of thermodynamics are satisfied. As a thermodynamical
whole, the evolution of the Undulant Universe behaves very well in the current
phase. However, when considering the unification theory, the failure of
conversation law at the epoch of the matter dominated or near singularity need
some more consideration for the form of the Undulant Universe.
