Nonlinear Dynamics and Stability Step by Step
A lightweight execution-visualization book.
Iteration Ledgers
Affine Map Keeps a Finite Ledger
Quadratic Map Stops Before Denominators Grow
Piecewise Map Records the Branch
Fixed Points and Local Stability
Fixed-Point Substitution Closes the Loop
Slope Less Than One Is a Local Contract
Slope Greater Than One Is Rejected
Period Snapshots
Two-Cycle Must Return and Not Stop
Fixed Point Cannot Spoof a Two-Cycle
Parameter Rows Are Finite Snapshots
Feedback Geometry and Final Audit
Saturating Feedback Checks the Branch
Cobweb Geometry Uses Ledger Points
Dynamics Audit Cites Every Source
Relation Cross-Scans
Fixed Candidate Substitution Cross-Scan
Stability Slope Threshold Cross-Scan
Iteration Depth Error Cross-Scan
Reflection Parameter Period Cross-Scan
Boundary Depth Scans
Logistic Fixed Residual Zero Scan
Stability Margin Boundary Scan
Tent Branch Boundary Scan
Saturating Clamp Boundary Scan
Reflection Return Gap Period Scan