On the iterative process
On the orbits of hat-functions
On the rotation sets for non-continuous circle maps.
On the speed of convergence of iteration of a function.
On the stability of chaotic functions
On the structure of minimal attraction centers of recurrent trajectories of continuous maps of the interval.
On the structure of the space of continuous maps with zero topological entropy
On topological sequence entropy and chaotic maps on inverse limit spaces.
Optimal bounds for the length of rational Collatz cycles
Path differentiation: further unification
A. M. Bruckner, R. J. O'Malley, and B. S. Thomson introduced path differentiation as a vehicle for unifying the theory of numerous types of generalized differentiation of real valued functions of a real variable. Part of their classification scheme was based on intersection properties of the underlying path systems. Here, additional light is shed on the relationships between these various types of path differentiation and it is shown how composite differentiation and first return differentiation...
p-convex iteration groups
Periodic orbits of maps with an infinite number of partition points.
Periodic points and bifurcation of one-dimensional maps
Periodic points, multiplicities, and dynamical units.
Periodic points of a continuous map of the interval
Progress of iteration theory since 1981.
Regular fractional iteration of convex functions
The existence of a unique solution φ of equation (1) is proved under the condition that f: I → I is convex or concave and of class in I, 0 < f(x) < x in I*, and f’(x) > 0 in I. Here I = [0, a] or [0, a), 0 < a ≤ ∞, and I* = I 0.
Regular fractional iterations.
Regular Iteration in the Case of Multiplier Zero
Remarks on iterated cubic maps.