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

Fujiwara, Akio; Amari, Shun-ichi

Physica D 80, No. 3, 317-327 (1995).

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.

MSC:

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)

Keywords:

information geometry; gradient flow; dualistic structure; dynamical systems

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