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The Relationship between Topological Entropy and
Pseudo-Orbits in Uniform Spaces
Ridzuwani Binti Abdul Rahim
Supervisor: Assoc. Prof. Dr. Zabidin Bin Salleh
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
Topological entropy measures the maximal exponential growth rate of different forward
orbits for an arbitrary topological dynamical systems and pseudo-orbits is it powerful
tools. We predict the relationship between pseudo-orbits entropy and topological entropy
and we describe the correlation between uniform spaces and topological entropy. Then,
justify description about uniform spaces and topological entropy and analyse about
pseudo-orbits and topological entropy. The methods are, let a uniform space be a set X
equipped with a uniform structure, collection of X × X each of which contains the diagonal
and some additional properties. The topological entropy of uniform spaces can be
calculated in terms of growth rate of pseudo-orbits. Let T ∶ X → X be a continuous map
of a compact uniform space (X, u) and we get h top (T) = h sep (T) = h span (T) and
h top (T) = h ψ (T) (the number h ψ (T) will be called the pseudo-orbit entropy of T). Hence,
the relationship between topological entropy and pseudo-orbits in uniform spaces are
shown.
1003 | UMT UNDERGRADUATE RESEARCH DAY 2018