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At a very low temperature of 9mK, electrons in the 2nd Landau level of anextremely high mobility two-dimensional electron system exhibit a very complexelectronic behavior. With varying filling factor, quantum liquids of differentorigins compete with several insulating phases leading to an irregular patternin the transport parameters. We observe a fully developed $\nu=2+2/5$ stateseparated from the even-denominator $\nu=2+1/2$ state by an insulating phaseand a $\nu=2+2/7$ and $\nu=2+1/5$ state surrounded by such phases. A developingplateau at $\nu=2+3/8$ points to the existence of other even-denominatorstates

Electron Correlation in the Second Landau Level: A Competition Between Many Nearly Degenerate Quantum Phases