What is a repeller in dynamical systems?

A repeller is an invariant set in a phase space that repels nearby trajectories, serving as a fundamental concept for understanding unstable equilibria and qualitative flows.

What is a non-backtracking geodesic qualification?

It is a condition ensuring that state invocation chains do not revisit previous states, utilizing Möbius filters and Ramanujan bounds for efficient expansion.

How does this skill use AlgebraicDynamics.jl?

It leverages AlgebraicDynamics.jl patterns to implement repellers as compositional dynamical systems, specifically using resource-sharing machine structures.

What does the Trit -1 (MINUS) signify?

In the context of this skill's GF(3) integration, the -1 trit represents a specific state in a triadic composition that must be conserved across skill triplets.

Repeller Dynamical Systems

Name: Repeller Dynamical Systems
Author: plurigrid

byplurigrid

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Data Science & ML

Models and analyzes invariant sets that repel nearby trajectories within complex dynamical systems and topological manifolds.

About

The Repeller skill enables Claude to perform advanced modeling and analysis of dynamical systems where specific invariant sets push nearby trajectories away. Grounded in Dynamical Systems Theory and Algebraic Dynamics, it provides tools for analyzing local behavior near equilibria, global limit sets, and parameter-dependent bifurcations. This skill is particularly useful for researchers and developers working with topological computing, Julia-based AlgebraicDynamics.jl implementations, and GF(3) triadic logic frameworks, where maintaining conserved system states and non-backtracking geodesic paths is critical.

Key Features

Qualitative bifurcation tracking for parameter-dependent changes
2 GitHub stars
GF(3) triadic logic support for conserved system states
Analysis of local behavior near equilibria and invariant sets
Non-backtracking geodesic qualification for complex pathing
Compositional modeling via AlgebraicDynamics.jl integration

Use Cases

Analyzing long-term qualitative dynamics in high-dimensional phase spaces
Simulating unstable equilibria in physical and chemical dynamical systems
Designing state-space trajectories for topological computing architectures

About

Key Features

Qualitative bifurcation tracking for parameter-dependent changes
2 GitHub stars
GF(3) triadic logic support for conserved system states
Analysis of local behavior near equilibria and invariant sets
Non-backtracking geodesic qualification for complex pathing
Compositional modeling via AlgebraicDynamics.jl integration

Use Cases

Analyzing long-term qualitative dynamics in high-dimensional phase spaces
Simulating unstable equilibria in physical and chemical dynamical systems
Designing state-space trajectories for topological computing architectures