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10 papers · 1 filter
Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain
JA Foxman, JM Robbins
The n-particle periodic Toda chain is a well known example of an integrable but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold singularities of the Tod…
The Maslov index and nondegenerate singularities of integrable systems
JA Foxman, JM Robbins
We consider integrable Hamiltonian systems in R^{2n} with integrals of motion F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical points of F where rank dF =…
Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
Jiri Vanicek
Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. This fact is us…
Old and young leaves on plane trees
William Y. C. Chen, Emeric Deutsch, Sergi Elizalde
A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees with a given…
The Positive Bergman Complex of an Oriented Matroid
Federico Ardila, Caroline Klivans, Lauren Williams
We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive B…
Curved Hexagonal Packings of Equal Disks in a Circle
B. D. Lubachevsky, R. L. Graham
For each k >= 1 and corresponding hexagonal number h(k) = 3k(k+1)+1, we introduce m(k) = max[(k-1)!/ 2, 1] packings of h(k) equal disks inside a circle which we call "the curved he…