Contributed lectures presented earlier at Winter School on Transformation Groups.
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This paper shows that entropy is a completer metric similarity invariant for the continuous ergodic group automorphisms of the two-dimensional torus.
Part I. We consider dynamical systems depending on parameters in various, both conservative and dissipative settings. For such systems integrability is defined as equivariance with respect to an appropriate torus action. Part II. We consider nearly integrable families of dissip…