16 citations · 40 across the 7 of their papers we have counts for
7 papers
Variations on a Theme of Collatz
Mario Bruschi, Francesco Calogero
Consider the recursive relation generating a new positive integer from the positive integer according to the following simple rules: if the integer $n_{\e…
A generalization of the Collatz problem and conjecture
M. Bruschi
We introduce an infinite set of integer mappings that generalize the well-known Collatz-Ulam mapping and we conjecture that an infinite subset of these mappings feature the remarka…
New Cellular Automata associated with the Schroedinger Discrete Spectral Problem
M. Bruschi
New Cellular Automata associated with the Schroedinger discrete spectral problem are derived. These Cellular Automata possess an infinite (countable) set of constants of motion.
Two Cellular Automata for the 3x+1 Map
M. Bruschi
Two simple Cellular Automata, which mimic the Collatz-Ulam iterated map (3x+1 map), are introduced. These Cellular Automata allow to test efficiently the Collatz conjecture for ver…
Integrable systems of quartic oscillators. II
M. Bruschi, F. Calogero
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with line…
Convenient parameterizations of matrices in terms of vectors
M. Bruschi, F. Calogero
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain rec…