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Has Kepler (or any other survey) found an exoplanet with a similar orbit as another exoplanet around the same star?
The current IAU definition of a planet requires that "a planet has cleared its neighborhood around its orbit".
Have there been any exoplanet discoveries that bring such a definition into question?
Mathematically, is there anything stopping 2 "planets" from existing in equilibrium in a similar orbit around a single star?
Two planets sharing their orbit is expected to be a rare configuration. Most configurations of 2 planets in 1 orbit are unstable. Only when one planet is in a Lagrange point of the other, are the orbits stable.
As of now (February 2017), there are no known co-orbital planets. We do know lots of smaller objects co-orbiting with planets (in our own solar system, there are thousands of Trojans in e.g. Jupiter's orbit).
There was a potential detection (Kepler-223), but on closer examination those planets were unlikely to be co-orbital.
