Dynamical Systems & Mapping Structure

Primes about the mathematical scaffolding of change and mapping: properties of functions and transformations (injectivity, surjectivity, eigenvalues, fixed points), and the state-space description of evolving systems (phase space, state transition, convergence, controllability, observability).

15 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Continuity — Smooth change without jumps.
• Controllability — Ability to steer system.
• Convergence — Movement toward stable state.
• Develops-From Relation — A later entity came to be by stage-wise transformation of a continuing predecessor, the same continuant passing through directed, qualitatively distinct stages under a generative rule.
• Eigenvalue And Eigenvector — A transformation's invariant directions and the scalars by which it stretches them.
• Fixed Point — A state a transformation leaves unchanged — self-consistency under update — organizing analysis into existence, uniqueness, stability, and basin of attraction.
• Frame of Reference — Observational perspective.
• Function (Mapping) — Relates inputs to outputs.
• Injectivity — A distinctness-preserving mapping in which distinct inputs never collide on one output.
• Manifold — A space that is locally flat but globally curved or topologically non-trivial.
• Observability — Infer internal state externally.
• Phase Space — All possible system states.
• Saddle Point — An equilibrium stable in some directions and unstable in others.
• State and State Transition — Captures system condition and evolution.
• Surjectivity — A coverage-guaranteeing mapping in which every element of the target is hit by some input, leaving no gap in the codomain.