Singular Points of Polynomial Darboux Systems
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DOI: 10.1007/s12346-019-00319-7
Abstract: We study the singular points of the differential systems of the form $$\dot{x}= x+P(x,y), \ \dot{y}=y+Q(x,y)$$x˙=x+P(x,y),y˙=y+Q(x,y) where P(x, y) and Q(x, y) are homogeneous polynomials of degree n. read more here.
Keywords: systems singular; points polynomial; singular points; polynomial darboux ... See more keywords
Preperiodic points of polynomial dynamical systems over finite fields
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DOI: 10.1142/s1793042124501124
Abstract: For a prime $p$, positive integers $r,n$, and a polynomial $f$ with coefficients in $\mathbb{F}_{p^r}$, let $W_{p,r,n}(f)=f^n\left(\mathbb{F}_{p^r}\right)\setminus f^{n+1}\left(\mathbb{F}_{p^r}\right)$. As $n$ varies, the $W_{p,r,n}(f)$ partition the set of strictly preperiodic points of the dynamical system induced… read more here.
Keywords: finite fields; polynomial dynamical; dynamical systems; points polynomial ... See more keywords