In addition to scarring described above, there are several similar phenomena, either connected by theory or appearance. First of all, when scars are visually identified, some of the states may remind of classical ''bouncing-ball'' motion, excluded from quantum scars into its own category. For example, a stadium billiard supports these highly nonergodic eigenstates, which reflect trapped bouncing motion between the straight walls. It has been shown that the bouncing states persist at the limit ℏ ℏ → → 0 , but at the same time this result suggests a diminishing percentage of all the states in the agreement with the quantum ergodicity theorems of Alexander Schnirelman, Yves Colin de Verdière, and Steven Zelditch. Secondly, scarring should not be confused with statistical fluctuations. Similar structures of an enhanced probability density occur even as random superpositions of plane waves, in the sense of the Berry conjecture. Furthermore, there is a genre of scars, not caused by actual periodic orbits, but their remnants, known as ghosts. They refer to periodic orbits that are found in a nearby system in the sense of some tunable, external system parameter. Scarring of this kind has been associated to almost-periodic orbits. Another subclass of ghosts stems from complex periodic orbits which exist in the vicinity of bifurcation points.