Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Poincaré recurrence theorem | Statement: [H-theorem, relatedConcept, Poincaré recurrence theorem]

Target entity: Poincaré recurrence theorem
Context triple: [H-theorem, relatedConcept, Poincaré recurrence theorem]

• A. Poincaré recurrence theorem chosen
  The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
• B. Poincaré–Birkhoff fixed-point theorem
  The Poincaré–Birkhoff fixed-point theorem is a fundamental result in dynamical systems and topology that guarantees the existence of at least two fixed points for certain area-preserving twist maps of an annulus.
• C. Poincaré–Bendixson theorem
  The Poincaré–Bendixson theorem is a fundamental result in the qualitative theory of dynamical systems that characterizes the possible long-term behaviors of trajectories in two-dimensional continuous flows, ruling out chaotic dynamics in the plane.
• D. Kakutani equivalence in ergodic theory
  Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
• E. Poincaré map
  The Poincaré map is a mathematical tool in dynamical systems theory that reduces continuous-time dynamics to a discrete map by tracking intersections of trajectories with a lower-dimensional surface.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.