  A recent conjecture of Morita predicts a lower bound in temperature $T$ of a
chaotic system, $T\geq (\hbar/2\pi)\Lambda$, $\Lambda$ being the Lyapunov
exponent, which was demonstrated for a one dimensional inverse harmonic
oscillator. In the present work we discuss the robustness of this demonstration
in an extended version of the above model, where the inverse harmonic
oscillator lives a in two dimensional noncommutative space. We show that,
without noncommutativity, Morita's conjecture survives in an essentially
unchanged way in two dimensions. However, if noncommutativity is switched on,
the noncommutativity induced correction terms conspire to produce, in classical
framework, a purely oscillating non-chaotic system without any exponential
growth so that Lyapunov exponent is not defined. On the other hand, following
Morita's analysis, we show that quantum mechanically an effective temperature
with noncommutative corrections is generated. Thus Morita's conjecture is not
applicable in the noncommutative plane. A dimensionless parameter $\sigma
=m\alpha\theta^2$, (where $m, \alpha, \theta$ are the particle mass, coupling
strength with inverse oscillator and the noncommutative parameter respectively)
plays a crucial role in our analysis.
