What is the difference between Saddle points and Lagrangian points between Earth and the Sun?

Question

I am studying MOND bubble effects in the Solar System (Paper). In "mond habitats.." (last reference) first page, the author says MOND bubbles reside on the saddle points but I fail to understand the differences from Lagrangian points. Can anyone explain this to me?

MarkImmerzeel · Answer

In case you still want to know, here is my two cents. In MOND (the paper you referenced uses TeVeS the relativistic cousin of MOND) the potential is modified due to the introduction of an acceleration parameter a0. At accelerations below this value MONDian behaviour takes over. This means that the saddle point of the potential between two bodies is shifted away from the purely Newtonian L1. See for example figure 7 in this report:
https://engineering.purdue.edu/people/andrew.d.cox.2/pubs/2016_AAS_CoxHow.pdf

What is the difference between Saddle points and Lagrangian points between Earth and the Sun?

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