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To my understanding, the idea behind the interplanetary transport network is that areas near heavy objects and their Lagrange points are accesible with comparatively little energy, for example one could more easily leave low earth orbit via one of the Earth-Moon Lagrange points.

I'm looking for a feeling about what "little energy" and "long travel times" might mean quantitatively.

Now, I understand there'll be no map of the then possible, ever shifting paths around the solar system - but is there some list of sample missions? (Is that the term?)

The papers I skimmed seemd to be very daunting on the math front. Are there easy rules to guesstimate the $\Delta V$ requirements if a probe hops from e.g. from low Earth orbit to L1 to away from the earth-moon system? With what velocity?

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Something like this, along with the associated article on Wikipedia, might help:

enter image description here

And if you "learn by doing" and are willing to have a bit of fun while you develop a sense of the "map" there's a boardgame (of all things) that treats this topic fairly accurately (at least if what you're looking for is some intuition about how the $\Delta\text{V}$ map feels in the context of space travel):

enter image description here

And NASA provides a "trajectory browser" that provides some of the same information which, though not in "map" form, is customizable to just about any "route" you can imagine.


And for fun, there's always this:

enter image description here

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Your picture with delta-V is not about low-energy transfer, but about classic Hohmann transfer orbits with some additional classic orbital maneuvers. Low-energy transfer is about using unstable chaotic trajectories near Lagrange points. The only needed classical stage is to move to LEO and then to fly near some L1 or L2 point of the local system at the chosen moment of time. –  osgx Mar 12 at 18:02
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