36 citations · 99 across the 6 of their papers we have counts for
7 papers
Paradoxical behavior in Collatz sequences
Olivier Rozier, Claude Terracol
On the set of positive integers, we consider the iterative process that maps to either or depending on the parity of . The Collatz conjecture…
Are the Collatz and abc conjectures related?
Olivier Rozier
The Collatz and conjectures, both well known and thoroughly studied, appear to be largely unrelated at first sight. We show that assuming the conjecture true is helpful…
Elongation and stability of a linear dune
O. Rozier, C. Narteau, C. Gadal +2
Compared to barchan dunes, the morphodynamics of linear dunes that elongate on a non-erodible bed is barely investigated by means of laboratory experiments or numerical simulations…
Periodicity in fields of elongating dunes
Cyril Gadal, Clément Narteau, Sylvain Courrech du Pont +2
Dune fields are commonly associated with periodic patterns that are among the most recognizable landscapes on Earth and other planetary bodies. However, in zones of limited sedimen…
Incipient bedforms in a bidirectional wind regime
Cyril Gadal, Clément Narteau, Sylvain Courrech du Pont +2
Most terrestrial sand seas form at `horse' latitudes, where the wind direction exhibits seasonal variation. Here, we extend the two-dimensional linear stability analysis of a flat…
Parity sequences of the 3x+1 map on the 2-adic integers and Euclidean embedding
Olivier Rozier
In this paper, we consider the one-to-one correspondence between a 2-adic integer and its parity sequence under iteration of the so-called "3x+1" map. First, we prove a new formula…
The 3x+1 problem: a lower bound hypothesis
Olivier Rozier
Much work has been done attempting to understand the dynamic behaviour of the so-called "3x+1" function. It is known that finite sequences of iterations with a given length and a g…