Embed a nonlinear system into a linear oneKoopman linearizationnarrower versions, nested under the line they refineKoopman linearization — click the line to read about it hereCarleman linearization, a narrower version of Koopman linearizationCarleman linearization, a narrower version of Koopman linearization — click the line to read about it hereCarleman-Fourier linearization, a narrower version of Koopman linearizationCarleman-Fourier linearization, a narrower version of Koopman linearization — click the line to read about it hereKoopman-von Neumann lift to phase-space densitiesKoopman-von Neumann lift to phase-space densities — click the line to read about it hereLevel-set exact linearizationLevel-set exact linearization — click the line to read about it hereHomotopy perturbation embeddingHomotopy perturbation embedding — click the line to read about it hereKoopman linearization — click the name to read about it hereKoopman linearizationCarleman linearization, a narrower version of Koopman linearization — click the name to read about it hereCarleman linearizationCarleman-Fourier linearization, a narrower version of Koopman linearization — click the name to read about it hereCarleman-Fourier linearizationKoopman-von Neumann lift to phase-space densities — click the name to read about it hereKoopman–von Neumann liftLevel-set exact linearization — click the name to read about it hereLevel-set exact linearizationHomotopy perturbation embedding — click the name to read about it hereHomotopy perturbation embeddingNonlinear initial-value problem — you start hereLinear ODE system — you finish here

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Where the routes meet

Every circle is drawn once. This step has no smaller object recorded inside it, so the strands between its two circles are the recorded ways of taking it — one strand per method.

All the starting points

6 recorded ways of doing Embed a nonlinear system into a linear one. Nothing smaller is recorded inside it, so there is no object in the middle to draw.

Everything on this figure that opens is open.

Of the routes that have been taken apart, 15 are built entirely from named slots, 15 hand off part of the work and finish the rest themselves, and 20 are one undivided act. None of the three is a defect; they are different things to reuse.

Every line on this figure, in words

The lines on this figure

  1. Koopman linearization
  2. Carleman linearization, a narrower version of Koopman linearization
  3. Carleman-Fourier linearization, a narrower version of Koopman linearization
  4. Koopman-von Neumann lift to phase-space densities
  5. Level-set exact linearization
  6. Homotopy perturbation embedding
  • Every line on this figure is one a recorded source takes.

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Where you are

Path

  1. Solve a nonlinear ODE dy/dt = F(y)
  2. Embed a nonlinear system into a linear one

Ways through: 6

Routes that skip it

No recorded route avoids this step.

Narrower kinds

Read the full write-up

Every step you can open

1 of these have an object recorded in the middle; the rest open into the methods that fill them.

What is on this map, counted

What is here, counted

147 nodes — 31 slots and 116 methods.

76 of the 147 link to a record in the Atlas, between them naming 89 records. The rest name papers and nothing else: this graph describes work the catalogue has not got yet, and the nodes with no record are the list of what a corpus pass has to go and read.

0 slots have no method recorded, and 32 methods have not been taken apart. Both are shown as what they are rather than left blank.

Every claim here rests on a source. This graph cites 140 papers; they and the 172 the Atlas cites alone are registered in one place, with what each reports and everywhere it is cited from. Papers