I understand the Interplanetary Transport Network allows for travel at low speeds between different planets in the solar system using very little energy. Is there flexibility in how long it would take to travel between planets (with the same orbital configuration) on ITN? Does the Δ𝑣 determine how long it would take to travel between different bodies?
Is there a minimum time it would take between Jupiter and/or Saturn to travel to Mars and/or Earth using the ITN?
A dynamic system, with at least 3 massive bodies, will have chaos that can, in theory, be exploited to reach (almost) arbitrary positions within said system at close to zero $\Delta v$ over very long time spans. This is the "Interplanetary Transport Network".
This sounds very alluring, but it's easy to be misled into believing this has much relevance to space-flight. It may often even be intentionally presented in a misleading manner.
The following models of trajectories are used in space-flight involved multiple bodies, with quickly diminishing returns for the additional "tricks" their increasing complexity contribute.
The patched conics approximation. A spacecraft is always assumed to be orbiting a single body, and when it reaches another one, the frame of reference is changed. For the solar system, this is usually very accurate, as the gravitational influence of the closest body is in almost any location dwarfing all the other ones.
The CR3BP, which takes into account the gravitational influence of two bodies at once. This is only really relevant close to the border regions of the patched conics approximation, but it give rice to some interesting artefacts such as Lagrangian points
True n-body physics.
The ITN deals with the effects of the third one. Unfortunately, the gravitational influence of the "third strongest" body or lower is extremely small in almost any part of the solar system.
We actually happen to live close to one of the regions where true n-body physics is measurable, that is, the region where the Earth, the Moon and the Sun all contribute some meaningful amount of gravity.
In particular, The Sun-Earth L-points SEL1 and SEL2 and the Earth-Moon L-points EML1 and EML2 can be shown to be connected with the low energy pathways of the ITN.
Beyond that region, the effects of the ITN become almost unmeasurable small. There's no point in space where the gravitational influence of the Earth, the Sun and Jupiter all have comparable influence. One of those three will always be much much weaker than the strongest one, leading to ITN pathways in the order of millions of years.
This has to be clearly stated, as many others fail to say so.
Often confused with the ITN is gravity assists. The difference is that they are actually relevant to space-flight, and can be adequately modelled by patched conics.
Those can be effectively used to trade transfer time for $\Delta v$ savings.
