OBSERVATION CHAMBER / ACTIVE
Symplectic Map Phase-Space Observatory
Iterate an area-preserving standard map and read its phase-space trace, rotation number, finite-time Lyapunov exponent, and finite-sample regime.
ROUTE 67 / PHASE SPACE / AREA-PRESERVING MAP
01 / ITERATE THE MAP
A discrete map on the phase-space torus
Drag to choose θ,p · arrows move · Space run/pause · S step · R reset
Canvas 2D is unavailable; the numeric observation contract remains available below.
Observation contract pn+1 = pn + K sin θn, θn+1 = wrap(θn + pn+1). The torus view wraps both coordinates modulo 2π.
The selected orbit is green. Cyan traces are a fixed finite ensemble. The map, metrics, and renderer run locally with no API or external library.
03 / READ THE INVARIANTS
Map readout
- Finite sample
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- Visible / total
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- Ensemble sample
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- Self-test
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K=0 regular and K=3 chaotic fixtures are checked at load.
Advanced diagnostics and acceptance checks
The finite sample is a classification aid. Positive FTLE marks separation in the measured window; it is not an infinite-time proof of chaos.
Observation report
Formula note
The standard map is pn+1 = pn + K sin θn, θn+1 = wrap(θn + pn+1, 2π). Its Jacobian is J = [[1 + K cos θ, 1], [K cos θ, 1]], so det J = 1. The rotation number is the unwrapped mean θ advance divided by 2π; FTLE is the mean logarithmic tangent-vector stretch.
OBSERVATION GUIDE
Touchpoints for observation
Start with REGULAR, then compare MIXED and CHAOTIC. The same area-preserving rule can show invariant-torus candidates, resonant islands, and a chaotic sea in a finite phase-space sample.
- Use K=0 REGULAR to check constant momentum and a stable rotation number.
- Use K=3 CHAOTIC to check a positive finite-time Lyapunov exponent and sensitive orbit trace.
- Use drag or keyboard input to change only the initial point. RESET returns to the mixed observation.
This is a finite browser model of the Chirikov standard map. It is not a measurement of a physical accelerator, plasma, or mechanical system.
Runs inside the browser with no upload and no registration.
OBSERVATION POLICY
This observatory runs a browser-local standard map. Parameters, calculations, reports, and images are not uploaded. It does not measure a visitor or a physical dynamical system.
Route
This chamber belongs to Dynamics and Signals.
PHASE SPACEBack to the Dynamics and Signals Route.