A point of period k of a function f is a point x such that f (x) = x but f (x) 6= x for any 0 < i < k. Let φk(f) denote the number of real points of period k of f . In the case that f is a quadratic polynomial, we develop an algorithm to explicitly characterize φk(f) in terms of the coefficients of f. We show the resulting characterization for k ≤ 6. The method extends to higher k and higher de...

In this survey we describe how the so-called Dold congruence arises in topology, and it relates to periodic point counting dynamical systems.

In this paper, we introduce the concept of central periodic points a linear system as which lies on orbits starting and ending at subgroup system. We show that set is bounded if only compact. Moreover, admits control containing identity element G then, points, coincides with its interior.