Scholarlink

<p>We consider a class of continuous-discontinuous piecewise differential systems formed by two polynomial Hamiltonian systems of degrees <i>m</i> and <i>n</i>, separated by the non-regular line <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L=L_1\cup L_2=\{(x,0):x\ge 0\}\cup \{(x,y):y=(\tan \alpha ) x\ge 0\}\)</EquationSource> </InlineEquation>. These piecewise differential systems are continuous on the line <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_1\)</EquationSource> </InlineEquation> and discontinuous on the line <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L_2\)</EquationSource> </InlineEquation>. We provide an upper bound for the maximum number of limit cycles that intersect the lines <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L_1\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(L_2\)</EquationSource> </InlineEquation> in one point. So we have solved the extension of 16th Hilbert problem to this class of differential systems. For some values of <i>m</i> and <i>n</i> this upper bound is reached.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Limit Cycles of Continuous-Discontinuous Piecewise Differential Systems Formed by Two Hamiltonian Systems and Separated by a Non-regular Line

  • 期刊论文

  • 发表日期：

    2026年4月17日

查看全文
  • Bruno Freitas,
  • Deysquele Ávila,
  • Fernanda Becatti,
  • Jaume Llibre

摘要

We consider a class of continuous-discontinuous piecewise differential systems formed by two polynomial Hamiltonian systems of degrees m and n, separated by the non-regular line \(L=L_1\cup L_2=\{(x,0):x\ge 0\}\cup \{(x,y):y=(\tan \alpha ) x\ge 0\}\) . These piecewise differential systems are continuous on the line \(L_1\) and discontinuous on the line \(L_2\) . We provide an upper bound for the maximum number of limit cycles that intersect the lines \(L_1\) and \(L_2\) in one point. So we have solved the extension of 16th Hilbert problem to this class of differential systems. For some values of m and n this upper bound is reached.