Scholarlink

<p>In this paper, we obtain the invariant curve theorem without assuming any twist condition for quasi-periodic reversible mappings, which depend on a small parameter. As an application, we apply the result to investigate the boundedness of all solutions for the semilinear Duffing equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ddot{x}+\varpi ^2x+f(x,\dot{x},t)=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>x</mi> <mo>¨</mo> </mover> <mo>+</mo> <msup> <mi>ϖ</mi> <mn>2</mn> </msup> <mi>x</mi> <mo>+</mo> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mover accent="true"> <mi>x</mi> <mo>˙</mo> </mover> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f(x,\dot{x},t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mover accent="true"> <mi>x</mi> <mo>˙</mo> </mover> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> quasi-periodic.</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

Existence of invariant curves for non-twist quasi-periodic reversible mappings with application

  • 期刊论文

  • 发表日期：

    2026年4月26日

查看全文
  • Yiru Hao,
  • Shuyi Wang,
  • Min Li

摘要

In this paper, we obtain the invariant curve theorem without assuming any twist condition for quasi-periodic reversible mappings, which depend on a small parameter. As an application, we apply the result to investigate the boundedness of all solutions for the semilinear Duffing equation \(\ddot{x}+\varpi ^2x+f(x,\dot{x},t)=0\) x ¨ + ϖ 2 x + f ( x , x ˙ , t ) = 0 with \(f(x,\dot{x},t)\) f ( x , x ˙ , t ) quasi-periodic.