Chirikov Standard Map
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Chirikov standard map at K=0.9716 --- mixed phase space with coexisting regular islands and chaotic sea, the paradigm of Hamiltonian chaos
Interpretation
Standard analysis sees: bounded / light-tailed; anti-persistent; time-irreversible (slow rise, sharp collapse). The atlas additionally detects Persistent Homology:max_h1_lifetime. It sits beside Critical Circle Map (Bronze Mean) in the atlas (standard-bank rank 63) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.09
asymmetry0.45
occupancy0.83
short-range corr0.52
long-range memory0.11
spectral colour0.50
periodicity0.38
complexity0.35
time-irreversibility0.11
volatility clustering0.50
multifractality0.23
dimensionality0.47
nonstationarity0.45
What the atlas adds
Persistent Homology:max_h1_lifetime+2.2z
reconstructed phase space contains a persistent topological loop (S¹) — a smooth simple limit cycle
Atlas-extreme metrics the standard bank can’t predict for this source
Laplacian:laplacian_evolutionary_index | -2.2z | bank-miss 2.0σ |
Composition
dtypefloat64
range[1.293, 4.99]
unique values16384 / 16384
mean ± std3.14 ± 1.39
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Chirikov_Standard_Map.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Chirikov_Standard_Map.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Chirikov_Standard_Map.png)
Inflation (Substitution) > barcode
/d_curve/Chirikov_Standard_Map.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Chirikov_Standard_Map.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Chirikov_Standard_Map.png)
Ulam Spiral (Sacks) > default
/default/Chirikov_Standard_Map.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Standard Map K=0.5 (Mixed) | 3.18 | |
| Fibonacci Quasicrystal | 4.44 | cross-origin |
| Critical Circle Map (Bronze Mean) | 4.51 |
Which Geometries Light Up
This source does not rank extreme on any metric.
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