During the last decade, studies using probabilistic methods (Marcov`process) failed to predict the player`s displacement in racket sports by apply (Me Garry and Franks, 1996). The huge amount of information necessary limits the prediction and reflects the complexity of duals sports. In contrast, theories of self-organization investigate complex systems and use collective variable to characterize invariance and change of collectives mode emerging through the interaction of its components. (Haken, 1983). In the line of the above perspective, the present study investigates tennis as a non-linear complex system. A first step is to identify a so-called collective variable that sums up the invariant features and the changes occurring in the behavior of the players. In tennis, the game makes the players go back to the middle of the baseline after they have moved away from it in order to return the ball. Thus, the tennismen exhibit unceasing to-and-fro displacements about that central "position". Therefore, such periodic motion may be ascribed theoretically to that of an oscillator. Moreover, in order to move in a proper fashion, the players must take into account their own position, as well as those of their opponent and of the ball. This reciprocal attending constitutes an informational linkage, so that theoretically, the two players represent a system formed by two coupled oscillators. A well-established property of coupled oscillators, whatever their nature and their scale, is phase synchronization (Pikovsky et al, 2001).Thus, the collective behavior of coupled oscillators is adeptly captured by their relative phase, a measure of their lead-lag relationship. Therefore, we hypothesize that phase lag or relative phase is a pertinent collective variable to characterize the modes of displacements exhibited by two tennis players during the game.
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