Gradient systems in view of information geometry. (English) Zbl 0883.53020

Summary: Dualistic properties of a gradient flow on a manifold \(M\) associated with a dualistic structure \((g,\nabla, \nabla^*)\) is studied from an information geometrical viewpoint. Some useful applications are also investigated.


53B05 Linear and affine connections
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
62A01 Foundations and philosophical topics in statistics
94A15 Information theory (general)
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