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- Volume_entropy abstract "The volume entropy is an asymptotic invariant of a compact Riemannian manifold that measures the exponential growth rate of the volume of metric balls in its universal cover. This concept is closely related with other notions of entropy found in dynamical systems and plays an important role in differential geometry and geometric group theory. If the manifold is nonpositively curved then its volume entropy coincides with the topological entropy of the geodesic flow. It is of considerable interest in differential geometry to find the Riemannian metric on a given smooth manifold which minimizes the volume entropy, with locally symmetric spaces forming a basic class of examples.".
- Volume_entropy wikiPageID "19346619".
- Volume_entropy wikiPageRevisionID "429217285".
- Volume_entropy hasPhotoCollection Volume_entropy.
- Volume_entropy subject Category:Differential_geometry.
- Volume_entropy subject Category:Dynamical_systems.
- Volume_entropy subject Category:Entropy.
- Volume_entropy subject Category:Ergodic_theory.
- Volume_entropy subject Category:Systolic_geometry.
- Volume_entropy type Abstraction100002137.
- Volume_entropy type Attribute100024264.
- Volume_entropy type DynamicalSystem106246361.
- Volume_entropy type DynamicalSystems.
- Volume_entropy type PhaseSpace100029114.
- Volume_entropy type Space100028651.
- Volume_entropy comment "The volume entropy is an asymptotic invariant of a compact Riemannian manifold that measures the exponential growth rate of the volume of metric balls in its universal cover. This concept is closely related with other notions of entropy found in dynamical systems and plays an important role in differential geometry and geometric group theory. If the manifold is nonpositively curved then its volume entropy coincides with the topological entropy of the geodesic flow.".
- Volume_entropy label "Volume entropy".
- Volume_entropy sameAs m.04mxzyr.
- Volume_entropy sameAs Q7940890.
- Volume_entropy sameAs Q7940890.
- Volume_entropy sameAs Volume_entropy.
- Volume_entropy wasDerivedFrom Volume_entropy?oldid=429217285.
- Volume_entropy isPrimaryTopicOf Volume_entropy.