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Description:
It seems to be very fruitful to introduce the concept of partner orbits and orbit clustering in theoretical physics to study universal spectral fluctuations of quantum systems within the semiclassical limit. However, a mathematically-rigorous treatment is still missing. We will introduce this phenomenon in the case of a hyperbolic dynamical system and study some properties from a geometrical point of view. Moreover, we will introduce partner orbits in symbolic dynamics and establish a structure of clustering periodic orbits using graph theory.