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 maps | Statement: [chaos theory, usesTool, Poincaré maps]

Target entity: Poincaré maps
Context triple: [chaos theory, usesTool, Poincaré maps]

• A. Poincaré map chosen
  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.
• B. Arnold cat map
  The Arnold cat map is a famous example of a chaotic, area-preserving transformation on the torus that illustrates how simple deterministic rules can produce complex, seemingly random behavior.
• C. 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.
• D. Smale horseshoe
  The Smale horseshoe is a fundamental example in dynamical systems theory that illustrates chaotic behavior through a specific stretching-and-folding map of a square into a horseshoe-shaped region.
• E. Lyapunov exponents
  Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.