Abstract For a polynomial progression $$ \begin{align*}(x,\; x+P_1(y),\ldots,\; x+P_{t}(y)),\end{align*} we define four notions of complexity: Host–Kra complexity, Weyl true complexity and algebraic complexity. The first two describe the smallest characteristic factor progression, third refers to smallest-degree Gowers norm controlling fourth concerns relations between terms progressions. We co...

Abstract Let $P_1,P_2,\dots , P_k$ be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or Chebyshev polynomials, and $S$ the semigroup under composition generated by P_k$. We show all elements share a measure maximal entropy if only intersection principal left ideals $SP_1\cap SP_2\cap \dots \cap SP_k$ is non-empty.

In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. particular, prove that the operator of Hörmander type is bounded from $${H^{{p_1}}} \times \cdots {H^{{p_m}}}$$ to Hp for 0 < p1, …, pm ≤ 1 with 1/p1+ ⋯ + 1/pm = 1/p, under suitable cancellation conditions. As a result, extend trilinear estimates in [17] general ones and improve boundedness result [18] limiting si...

We study coexistence in discrete time multi-type frog models. first show that for two types of particles on $\mathbb{Z}^d$, $d\geq2$, any jumping parameters $p_1, p_2 \in (0,1)$, occurs with positive probability sufficiently rich deterministic initial configuration. extend this to the case random distribution particles. question multiple and $2^d$ $\mathbb{Z}^d$ enough also an instance infinite...

In this paper we determine the generalized Weierstrass semigroup $$ \widehat{H}(P_{\infty }, P_1, \ldots , P_{m})$$ and consequently $$H(P_{\infty at $$m+1$$ points on curves $$\mathcal {X}_{a,b,n,s}$$ {Y}_{n,s}$$ . These has been introduced in Tafazolian et al (J Pure Appl Algebra 220:1122–1132, 2016) as new examples of which cannot be covered by Hermitian curve.

We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$ arbitrary coefficients, $N\in \mathbb N$. For $N=2$, being both $\gamma_1,\gamma_2$ different from zero, this reduces to Zernike system. prove that $\mathcal H...