Dualism in Bitcoin Dynamics: existence of an Upper Bound in Poincaré Recurrence Theorem for Deterministic vs Stochastic Behavior

In this paper we want to describe a model of the dynamics of the Bitcoin cryptocurrency system. We can define a duality in these dynamics: Bitcoin mostly behaves as a deterministic system and in some time intervals, much shorter, it enters a stochastic regime. In particular, using Poincaré’s recurrence theorem, it was possible to study when the transition from one regime to another occurs. Furthermore, by applying our hypothesis to real data it was possible to explain a reason why the Bitcoin system is affected by such a "high volatility".