14 problems

Let $F(x,y)=\left(y,\frac{a+y}{x}\right)$ with $a>0$ act on ${\cal U}=\{(x,y)\in\mathbb{R}^2:x>0,y>0\}$. The map has a first integral $V$, whose level curves are topological circle…

An invariant variety of periodic points is a variety determined uniquely by the invariants of a map, whose points are periodic with a fixed period. Invariant-variety conjecture. If…

Let $\mathcal{G}$ be the Lie group of nonlocal symmetry diffeomorphisms associated with the integrable map … . Let its Lie algebra of generators be the Lie algebra of the correspon…

The integrable map corresponding to the linear equation, respectively the nonlinear equation, is denoted by … . A nonlocal diffeomorphism is a diffeomorphism whose action is nonloc…

Saddle-point conjecture. The fixed point $E_2$ is always a saddle point if it exists, that is,

Let $W_{\textrm{loc}}^{\textup{c}}(0)$ be the local center manifold from Theorem … can be combined with the results on regular fold points to describe certain properties of the geo…

Discrete dynamical system conjecture. The semigroup ${\rm S}$ may be obtained as the limit

Let $X_t,Y_t\geq 0$ evolve according to the competitive Ricker map … where $K,L>0$ are the carrying capacities and $a,b>0$ are the competitive factors. Global stability conjecture.…

Bifurcation-diagram conjecture. Contrarily to integer-order maps, determining the bifurcation diagrams of fractional-order maps is far from being a clarified problem.

Let a QP differential system be given, and consider the multiplicative and additive discretizations … के and … where each $\varphi_i$ is differentiable. Commutativity conjecture. F…

Let $T\geq 3$ and $N\geq 1$ be integers. Let $I_N^{(T)}$ and $P_N$ be the quantities defined in the paper. Bound conjecture. … This is proposed in connection with the preceding est…

Periodic-orbit conjecture. For every real $\lambda$ with $|\lambda|<2$, all orbits of $F$ are periodic.

Let finite-time average velocities be those associated with the random discrete dynamical systems under consideration, and let the local velocities be random with the setting descr…

A dynamical system is almost cooperative if its cooperativity condition holds except possibly for a single pair $i\not=j$; in the continuous case, the condition is…