Skill

dynamical-system-functor

From asi

Provides categorical framework for dynamical systems, analyzing phase spaces, local/global behavior, bifurcations, stability, and flows on manifolds. Useful for theoretical dynamics modeling.

ai-ml

npx claudepluginhub plurigrid/asi --plugin asi

Tool Access

This skill uses the workspace's default tool permissions.

Preview

**Trit**: 1 (PLUS)

SKILL.md

Similar Skills

flow

Explains flows as one-parameter groups of diffeomorphisms generated by vector fields in dynamical systems theory. Useful for analyzing ODEs, equilibria, stability, bifurcations, and long-term dynamics.

asi

cache-components

139.3k

Guides Next.js Cache Components and Partial Prerendering (PPR): 'use cache' directives, cacheLife(), cacheTag(), revalidateTag() for caching, invalidation, static/dynamic optimization. Auto-activates on cacheComponents: true.

cache-components

mcp-builder

124.2k

Guides building MCP servers enabling LLMs to interact with external services via tools. Covers best practices, TypeScript/Node (MCP SDK), Python (FastMCP).

9 files

anthropics-skills-13

Stats

Parent Repo Stars16

Parent Repo Forks5

Last CommitFeb 16, 2026

Used By2 plugins

Actions

View Source View Plugin View on GitHub View README

Help us improve

Share bugs, ideas, or general feedback.

Dynamical System Functor

Trit: 1 (PLUS) Domain: Dynamical Systems Theory Principle: Categorical structure of dynamical systems

Overview

Dynamical System Functor is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.

Mathematical Definition

DYNAMICAL_SYSTEM_FUNCTOR: Phase space × Time → Phase space

Key Properties

Local behavior: Analysis near equilibria and invariant sets
Global structure: Long-term dynamics and limit sets
Bifurcations: Parameter-dependent qualitative changes
Stability: Robustness under perturbation

Integration with GF(3)

This skill participates in triadic composition:

Trit 1 (PLUS): Sources/generators
Conservation: Σ trits ≡ 0 (mod 3) across skill triplets

AlgebraicDynamics.jl Connection

using AlgebraicDynamics

# Dynamical System Functor as compositional dynamical system
# Implements oapply for resource-sharing machines

Related Skills

equilibrium (trit 0)
stability (trit +1)
bifurcation (trit +1)
attractor (trit +1)
lyapunov-function (trit -1)

Skill Name: dynamical-system-functor Type: Dynamical Systems / Dynamical System Functor Trit: 1 (PLUS) GF(3): Conserved in triplet composition

Non-Backtracking Geodesic Qualification

Condition: μ(n) ≠ 0 (Möbius squarefree)

This skill is qualified for non-backtracking geodesic traversal:

Prime Path: No state revisited in skill invocation chain
Möbius Filter: Composite paths (backtracking) cancel via μ-inversion
GF(3) Conservation: Trit sum ≡ 0 (mod 3) across skill triplets
Spectral Gap: Ramanujan bound λ₂ ≤ 2√(k-1) for k-regular expansion

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)