A concept of entropy production associated with continuous topolog-ical evolution is deduced (without statistics) from the fact that Cartan-Hilbert 1-form of Action defines a non-equilibrium symplectic system of Pfaff Topological dimension 2n+2. The differential entropy, dS, is composed of the interior product of the non-canonical components of momentum with the components of the differential v...

Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required). This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1) it does not require the space to be compact and, thus, generalizes Adler, Konhe...

On the background of a brief survey panorama results on topic in title, one new theorem is presented concerning positive topological entropy (i.e. chaos) for impulsive differential equations Cartesian product compact intervals, which positively invariant under composition associated Poincaré translation operator with multivalued upper semicontinuous mapping.

Let X1, X2 be mixing connected algebraic dynamical systems with the descending chain condition. We show that every equivariant continuous map X1 → X2 is affine (that is, X2 is topologically rigid) if and only if the system X2 has finite topological entropy.