Definition 2.1 ([1]) A point p ∈ X and the trajectory through it are unpredictable if there exist a positive number ϵ$_{0}$ (the sensitivity constant) and sequences { t$_{n}$ } and { τ$_{n}$ } , both of which diverge to infinity, such that lim n $_{→∞}$π ( t$_{n}$, p ) = p and d [ π ( t$_{n}$ + τ$_{n}$, p ) , π ( τ$_{n}$, p )] ≥ ϵ$_{0}$ for each n ∈ N . An important point to discuss is the sensitivity or unpredictability. In the famous research studies [2, 3, 10, 11, 12], sensitivity was considered as a property of a system on a certain set of initial data since it compares the behavior of at least couples of solutions. Definition 2.1 allows to formulate unpredictability for a single trajectory. Indicating an unpredictable point p, one can make an error by taking a point π ( t$_{n}$, p ) . Then d [ π ( τ$_{n}$, π ( t$_{n}$, p )) , π ( τ$_{n}$, p )] ≥ ϵ$_{0}$, and this is unpredictability for the motion. Thus, we say about the unpredictability of a single trajectory whereas the former definitions considered the property in a set of motions. It was proved in [1] that if p ∈ X is an unpredictable point, then T ( p ) is neither a rest point nor a cycle, and that if a point p ∈ X is unpredictable, then every point of the trajectory T ( p ) is also unpredictable. It is worth noting that the sensitivity constant ϵ$_{0}$ is common for each point on an unpredictable trajectory. The dynamics on a set S ⊆ X is sensitive [3, 11] if there exists a positive number ϵ$_{0}$ such that for each u ∈ S and each positive number δ there exist a point u$_{δ}$ ∈ S and a positive number τ$_{δ}$ such that d [ u$_{δ}$, u ] < δ and d [ π ( τ$_{δ}$, u$_{δ}$ ) , π ( τ$_{δ}$, u )] ≥ ϵ$_{0}$. A result concerning sensitivity in a quasi-minimal set is given in the next theorem. Theorem 2.2 ([1]) The dynamics on Θ$_{p}$ is sensitive if p ∈ X is an unpredictable point. Theorem 2.2 mentions the presence of sensitivity in the set Θ$_{p}$ if p is an unpredictable point in X. Ac- cording to Theorem 2.1, if the trajectory T ( p ) of an unpredictable point p ∈ X is contained in a compact subset of X, then Θ$_{p}$ contains an uncountable set of everywhere dense stable P + motions. Additionally, since T ( p ) is dense in Θ$_{p}$ , the transitivity is also valid in the dynamics. Therefore, summarizing the last discussions, we propose a new definition of chaos based on the concept of the unpredictable point. This section is devoted to the description of unpredictable functions and their connection with chaos. For that purpose the results provided in [4] will be utilized. Let us denote by C ( R ) the set of continuous functions defined on R with values in R $^{m}$, and assume that C ( R ) has the topology of uniform convergence on compact sets, i.e., a sequence { h$_{k}$ } in C ( R ) is said to converge to a limit h if for every compact set U ⊂ R the sequence of restrictions { h$_{k}$ | U } converges to { h | U } uniformly. 3 3 Unpredictable Functions and Chaos