Algebraic and topological entropy on Lie groups
This paper starts with some examples and quick results on the topological entropy of continuous functions. It discusses the topological entropy on Lie groups and proves their shift properties. It proves Fried's conjecture h(phigamma) less than or equal to h(phi) + h(gamma) for affine maps on Lie groups. Moreover, phi and gamma do not have to commute. As a corollary, it proves that entropy is invariant with isometric endomorphisms of Lie groups. Also, it discusses algebraic entropy on elementary Abelian groups and Lie groups. It proves that the topological entropy is preserved when projected from Lie group R to its quotient space compact Lie group S-1 for continuous functions lifted from the quotient space and shows that algebraic entropy in general is strictly less than topological entropy. (C) 2004 Elsevier Ltd. All rights reserved.
topological entropy entropy lie group algebraic entropy