Recent advances in camera architectures and associated mathematical representations now enable compressive acquisition of images and videos at low data-rates. In such a setting, we consider the problem of human activity recognition, which is an important inference problem in many security and surveillance applications. We propose a framework for understanding human activities as a non-linear dynamical system, and propose a robust, generalizable feature that can be extracted directly from the compressed measurements without reconstructing the original video frames. The proposed feature is termed recurrence texture and is motivated from recurrence analysis of non-linear dynamical systems. We show that it is possible to obtain discriminative features directly from the compressed stream and show its utility in recognition of activities at very low data rates.