Iteration theory has its roots in the operation of substituting functions into itself. This has led to questions like that of the behaviour of functions by repeating this substitution and when the number of iterations tends to infinity. The terms 'orbit' and 'chaos' appropriately describe this behaviour. Dynamical systems and the theory of functional equations play important roles in this field.
Topological invariants for bimodal maps, P. Almeida et al; omega-limit
sets for smooth maps, F.B. Gallego and C.L. Paz; disappearance of a dovetail
structure in the parameter plane of a one-dimensional map, J.P. Carcasses;
contact bifurcations of absorbing areas and chaotic areas in two-dimensional
endomorphins, L. Gardini et al; properties of invariant areas in
two-dimensional endomorphisms, L. Gardini et al; an asymptotic formula for
the iterates of a function and related functional equations, D. Gronau; the
group of formal diffeomorphisms of the line and iteration theory, A.
Kholodov; strange attractors in cellular automata, H. Langenberg; qualitative
modifications of the "lip"-bifurcation structure, C. Mira and H. Kawakami;
chaotic control, M. Moran; the convergence of fast Pilgerschritt
transformation, N. Netzer; iteration groups of continuous functions
possessing fixed points, J. Tabor; and other papers.
