Closed trajectory in phase space
Trit: 0 (ERGODIC) Domain: Dynamical Systems Theory Principle: Closed trajectory in phase space
Periodic Orbit is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
PERIODIC_ORBIT: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Periodic Orbit as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: periodic-orbit Type: Dynamical Systems / Periodic Orbit Trit: 0 (ERGODIC) GF(3): Conserved in triplet composition
Condition: μ(n) ≠ 0 (Möbius squarefree)
This skill is qualified for non-backtracking geodesic traversal:
Geodesic Invariant:
∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
Möbius Inversion:
f(n) = Σ_{d|n} g(d) ⟹ g(n) = Σ_{d|n} μ(n/d) f(d)