in this paper, the functional properties of the recreational environment are substantiated using the example of biosphere ecological concept and ecosystem's framework approach for the sustainable development of territorial recreation systems (TRS). In the issue of the sustainable development of TRS, its makes sense to study the dynamic processes in the prism of natural and man-made systems. Under the natural-technogenic system, the authors understands the dynamic spatiotemporal range of both natural and anthropogenic materials and processes, through which the exchange of matter and energy in the local systems, including recreation ones, occurs. According to the authors, the buffer capacity of recreation system is the dominant factor determining the prospects for the sustainable development of TRS. The combination of theoretical and methodological foundations of the doctrine of functionally integral geosystems with the concept of multi-vector nature of recreational environment formation, allowed pointing out and specifying those TRS, which operate within a certain space. TRS, according to the authors is a dynamic set with the purpose of anthropogenic subjects and processes recreation within Geosystems whose activities continually trigger environmental changes, quantitative and qualitative Geosystem parameters, and is under the influence of man-made changes. The sustainable development of TRS provides an organization of recreational activities in which territorial Geosystem does not go beyond homeostasis and increasing of a recreational load is limited by buffer capacity of TRS. In this paper, the mathematical formalization of sustainable development of TRS is suggested. It can be used for the following definition of the subject of research: territorial recreational system that operates in the environment, is the set of subjects that formed from a set of internal components interconnected with each other and with the environment by set of connections which vary in the process of sustainable development in time and space according to the set of functions.