ON THE COMPLEXITY AND DIMENSION OF CONTINUOUS FINITE-DIMENSIONAL MAPS

摘要

We introduce the concept of ε-complexity of an individual continuous finite-dimensional map. This concept is in good accord with the principle of A.N. Kolmogorov's idea of measuring complexity of objects. It is shown that the ε-complexity of an "almost all" H?lder map can be effectively described. This description can be used as a basis for a model-free technique for segmentation and classification of data of arbitrary nature. A new definition of the dimension of the graph of a map is also proposed.