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Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

9 votes

If you were to axiomatize the notion of entropy

In addition to the wikipedia page, you can take a look at this fairly recent paper "A Characterization of Entropy in Terms of Information Loss" by John C. Baez, Tobias Fritz, Tom Leinster http://arxiv …
Anthony Leverrier's user avatar