One of the central themes in ergodic theory and dynamical systems is that of recurrence, which is a circle of results concerning how points in measurable dynamical systems return close to themselves under iteration. There are several types of recurrent behavior (exact recurrence, Poincaré recurrence, coherent recurrence , strictly coherent recurrence) for some classes of measurability-preserving discrete time dynamical systems. The second of these, which is the type originally introduced by Jules Henri Poincaré (published in 1890) and is still by far the most widely discussed, especially in physics, holds for all weakly mixing transformations (and so for all classes of weakly/strongly mixing dynamical systems with discrete time) by virtue of the fact that they are measure-preserving. Poincaré had shown that almost all points in a space subject to a measure-preserving transformation return over and over again to positions arbitrarily close to their original position. However, P. Johnson  and A. Sklar in  [J. Math. Anal. Appl. 54 (1976), no. 3, 752-771] regard the third type („ coherent recurrence” for measurability-preserving transformations) as being of at least equal physical significance, and this type of recurrence fails for Čebyšev polynomials. They also found that there is considerable evidence  to support a conjecture that no (strongly) mixing transformation can exhibit coherent recurrence. (This conjecture has been proved by R. E. Rice in [Aequationes Math. 17 (1978), no. 1, 104-108].)