Rotation intervals and entropy on attracting annular continua

Rotation and Entropy

For a given map f : X → X and an observable φ : X → Rd, rotation vectors are the limits of ergodic averages of φ. We study which part of the topological entropy of f is associated to a given rotation vector and which part is associated with many rotation vectors. According to this distinction, we introduce directional and lost entropies. We discuss their properties in the general case and analy...

Directional Entropy of Rotation Sets

Geometry and Entropy of Generalized Rotation Sets

For a continuous map f on a compact metric space we study the geometry and entropy of the generalized rotation set Rot(Φ). Here Φ = (φ1, ..., φm) is a m-dimensional continuous potential and Rot(Φ) is the set of all μ-integrals of Φ and μ runs over all f -invariant probability measures. It is easy to see that the rotation set is a compact and convex subset of R. We study the question if every co...

Friction, Free Axes of Rotation and Entropy

Friction forces acting on rotators may promote their alignment and therefore eliminate degrees of freedom in their movement. The alignment of rotators by friction force was shown by experiments performed with different spinners, demonstrating how friction generates negentropy in a system of rotators. A gas of rigid rotators influenced by friction force is considered. The orientational negentrop...

Entropy and Rotation Sets: a Toymodel Approach

Given a continuous dynamical system f on a compact metric space X and a continuous potential Φ : X → R, the generalized rotation set is the subset of R consisting of all integrals of Φ with respect to all invariant probability measures. The localized entropy at a point in the rotation set is defined as the supremum of the measuretheoretic entropies over all invariant measures whose integrals pr...