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math.DS2024
Mathematical and physical billiard in pyramids
Yury Kochetkov, Lev Pyatko
In this experimental work we study billiard trajectories in triangular pyramids and try to establish conditions that guarantee the existence (or absence) of 4-cycles (there can be…
math.DS2016
Plane trees, Shabat-Zapponi polynomials and Julia sets
Yury Kochetkov
A tree, embedded into plane, is a dessin d'enfant and its Belyi function is a polynomial --- Shabat polynomial. The Zapponi form of this polynomial is unique, so we can correspond…