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The Relations between Topology Entropy and Algebraic
Entropy by Pontryagin Duality
Nurin Nafisah Binti Mohd Khiri
Supervisor: Assoc. Prof. Dr. Zabidin Bin Salleh
Bachelor of Science (Financial Mathematics)
School of Informatics and Applied Mathematics
The Pontryagin dual Ĝ of G is the group of all continuous homomorphisms G→T,
endowed with the compact-open topology. If φ: G ⟶ G is a continuous
endomomorphism, its dual endomorphism. φ̂: Ĝ ⟶ Ĝ is defined by φ̂(X) = X o φ for every
XεĜ. The Pontryagin dual of abelian group is always compact. The objective of this
research is to describe the Pontryagin duality that connect the topological and the
algebraic entropy. In addition, there must have further investigation about Yuzvinski
Formula and Addition Theorem .Third, to prove the Bridge Theorem for the case of
connection between topology entropy and algebraic entropy. The result of this research
is topology entropy and algebraic entropy are connected by Pontryagin duality theorem
which they have a properties that shown similarities of both entropies. To be more clear,
it is used Yuzvinski Formula and Addition Theorem as ingredients to proof Bridge
Theorem. Using this properties, thus Bridge Theorem have been prove.
871 | UMT UNDERGRADUATE RESEARCH DAY 2018