It looks like the Hildas can run asymmetrically.  
Try this one  
ln(3.793667894) / ln(2)
So that 1.333333333333 / 0.69314718 = 1.923593388
2^1.923593388

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In the simulations, they can't interact.  The Hildas and Trojans are massless particles.  In the real solar system they are not massive enough to have appreciable gravity, so they don't interact either.  I doubt they can swap since their semi-major axes are totally different.
 
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I'm not quite sure what you're doing here?
 
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There are no Hildas in the simulation that made this animation.  Even if there were, they would be massless and unable to affect anything.
The "breathing" effect is from Jupiter's eccentricity.

One possibility , without having analysed the full paper content ,  if we assume the trojan scenario , is that the first dip at 800 days may be due to giant planet transit . The irregular dips at around 1550 days may be due to a trojan swarm transit either leading or trailing . This means 750 days between the trojans and the giant planet ( 60°) . This means a period for the planet of about 6*750 days = ca. 4500 days .
Assuming the mass of the star having 1.43 solar mass ( wiki ) , we get an SMA for the planet of 6 AU.
Orbital period and SMA are same order as our Jupiter  .  
If the hypothesis is correct the light curve should show dips  around about 50 days ( a few are there)  
Edit the following sentence is incorrect: or at 1550+750=2300 ( no data available ) .  
.  
I don't know if the trojans can have enough mass (or surface) to explain the rather serious dips.  
 
Edit : checking the transit time of the hypothetical planet which would cause the dip in the light curve at ca. 800 days , assuming it being at 6AU gives a transit time of about 1.3 days . This might correspond to the dip in the light curve at ca. 800 days , which seems to be in the order of 1.5-2 days .

Yes , a lot more trojans than in our solar system , is one possibility .  
Another possibility are coorbitals.
It may be possible that the supposed gas giant has some coorbital planets in the same orbit . Such a system has a lot of dynamical behaviour .
I remember once having simulated our Earth having up to five or six companions in the same orbit .  
AFAIR the system was stable in SMA , but showed a lot of dynamics , meaning planets moving towards each other in their orbit quite close .
Maybe Tony joins in here to express his experience ..

To illustrate the dynamical behaviour of possible coorbitals :  
hereby an animation I created some years ago , of 6 Earth planets originally positioned at 60° in our solar system  
After a while the system gets excited  ie chaotical in Mean Anomaly , but preserving the SMA to the central star .  
Such a system resembles a trojan system , but with the difference  the notion of L4 and L5 points becomes irrelevant , because every coorbital may in fact be found  outside the L4 and L5 points.  
 

Won't it work rather like a pair of tinted glasses? I've got a pair of tinted glasses, which are barely tinted, looking out of them there's next to no change in light, but seen from twenty metres away, people see the tint. Here we're talking about a few A.U's but now the people are standing 1400 light years away.  
 
Neptune has ten times as many 1km diameter Trojans as Jupiter, that's the estimate according to Wiki.  Their density suggests that they are basically dirty ice. Their relative velocities are so low that they can just stick together. It might well be that dumbbell comets come from that swarm. But back to Jupiter's Trojans and Hildas, they knock chunks off each other over four billion years but do they grind each other to dust? Mightn't it be the case that very small fragments, from collisions, build up slightly larger fragments over time? So that we have building and demolition going on constantly.
 
We could just wait and see what SETI says; they say a paper will be out in about a month or so, but it would be a laugh to pip them to the post.

frankuitaalst, do your co-orbital planets start out as that? We have just a lot of dust which needs to form into a planet. So does it do that, then migrate; with several others into the co-orbital configuration?  
 
I've never been a great fan of the idea of some co-orbital, the size of Mars, forming, then being deflected by Venus and Mercury into hitting a proto-Earth. Too much of a good thing for NASA's graphic designers I fear. I actually prefer Darwin's theory. A proto-Earth, a gas giant the size of Jupiter, throws out Mars as it condenses, and needs to dump angular momentum.