In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

We consider the class of interval maps with dense set of periodic points CP and its closure
Cl (CP) equipped with the metric of uniform convergence. Besides studying basic …

We prove that if a mixing map $ f:[0, 1]\to [0, 1] $ belongs to the ${C^ 0} $-closure of the set of
iterates and $ f (0)\ne 0$, $ f (1)\ne 1$ then $ f $ is an iterate itself. Together with some one …

For the generic continuous map and for the generic homeomorphism of the Cantor space,
we study the dynamics of the induced map on the space of probability measures, with …

In this article we introduce a generalization of the concept of equicontinuity, namely the
concept of Equi-Baire one for a family of functions on metric spaces. We use this concept to …

Let f: X→ X be a continuous map on the compact metric space X. Of considerable interest
and importance in dynamical systems are minimal sets. A set is minimal for f if it is a minimal …

SJ Agronsky, AM Bruckner, and M. Laczkovic have studied the behaviour of the sequence
$({f^ n}(x)) $ where f is the typical continuous function from the closed unit interval I into itself …

TOPICAL SURVEY Applications of the Baire Category Theorem Page 1 TOPICAL SURVEY
Real Analysis Exchange Vol. 23(2), 1997/8, pp. 363–394 Sara Hawtrey Jones, Department of …

Let K be the class of compact subsets of a metric space (X, ρ), furnished with the Hausdorff
metric. Here, we study the dynamics of the limit function of a sequence of functions {fn} n …

Abstract Let I=[0, 1], and let b⁢ B 1 be the set of Baire-1 self-maps of I. For f∈ b⁢ B 1, let
Λ⁢(f)=⋃ x∈ I ω⁢(x, f) be the set of ω-limit points of f. We prove the following:(i) There exists a …