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Define the following order among all natural numbers except for 2 and 1: [ 4gg 6gg 3gg dots gg 4ngg 4n+2gg 2n+1gg 4n+4ggdots ] Let $f$ be a continuous interval map. We show that if $mgg s$ and $f$ has a cycle with no division (no block structure) of period $m$ then $f$ has also a cycle with no division (no block structure) of period $s$. We describe possible sets of periods of cycles of $f$ with no division and no block structure.
A tournament H is quasirandom-forcing if the following holds for every sequence (G_n) of tournaments of growing orders: if the density of H in G_n converges to the expected density of H in a random tournament, then (G_n) is quasirandom. Every transit
A cyclic permutation $pi:{1, dots, N}to {1, dots, N}$ has a emph{block structure} if there is a partition of ${1, dots, N}$ into $k otin{1,N}$ segments (emph{blocks}) permuted by $pi$; call $k$ the emph{period} of this block structure. Let $p_1<dots
We consider a class of parametrically forced Hamiltonian systems with one-and-a-half degrees of freedom and study the stability of the dynamics when the frequency of the forcing is relatively high or low. We show that, provided the frequency of the f
We introduce the study of forcing sets in mathematical origami. The origami material folds flat along straight line segments called creases, each of which is assigned a folding direction of mountain or valley. A subset $F$ of creases is forcing if th
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold. When both pa