The topology of centered cylinder sets and block permutations, give us a way for knowing and classifying different kinds of basic dynamical behaviors in reversible one dimensional cellular automata. We have used very simple matrix methods for finding periodical and transitive behavior in such systems.
As we said at the end of section 5, this matrix methods detect the existence of such behaviors, but they don't show an explicit example of every behavior. The classification proposed in this paper is for automata whose invertible evolution rules have the same nighborhood size, and we have used the representation of any reversible one dimensional cellular automaton with another with neighborhood size equal 
.
This causes that the number of states has a considerably grow. In this way, these methods are easy for computing if the number of states is small.
Experimental observations show that Welch indices are not fundamental for establishing that a given reversible one dimensional cellular automaton belongs to a particular dynamical class. As we see in section 7, a same class has automata with different Welch indices.
Until now, all the automata generated in experimental observations are topologically ergodic and topologically mixing, that is, there exists orbits from every centered cylinder set to all the others. This could be explained by the action of the shift between block permutations, this shift allows that a centered cylinder set can reach a bigger number of centered cylinder sets.
In 
reversible one dimensional cellular automata, a preliminary examination shows only kinds of dynamical classes. The first classification has 
classes, 
with 
elements and 
with 
element each one. The second classification has 
classes, 
of 
elements and with elements. Another question is which is the influence of the uniform multiplicity both in connectivity and transition relations, i.e., in which way the uniform multiplicity establishes the quantitative behavior of the connections that every centered cylinder set has to.