Scholarlink

<p>We prove that cubic polynomial maps with a fixed Siegel disk and a critical orbit eventually landing inside that Siegel disk lie in the support of the bifurcation measure <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu _{\textrm{bif}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>μ</mi> <mtext>bif</mtext> </msub> </math></EquationSource> </InlineEquation>. This answers a question of Dujardin in positive. Our result implies the existence of holomorphic disks in the support of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mu _{\textrm{bif}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>μ</mi> <mtext>bif</mtext> </msub> </math></EquationSource> </InlineEquation>, and also implies that the set of rigid parameters is not closed in the moduli space of cubic polynomials.</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

Cubic Siegel Polynomials and the Bifurcation Measure

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月7日

查看全文
  • Matthieu Astorg,
  • Davoud Cheraghi,
  • Arnaud Chéritat

摘要

We prove that cubic polynomial maps with a fixed Siegel disk and a critical orbit eventually landing inside that Siegel disk lie in the support of the bifurcation measure \(\mu _{\textrm{bif}}\) μ bif . This answers a question of Dujardin in positive. Our result implies the existence of holomorphic disks in the support of \(\mu _{\textrm{bif}}\) μ bif , and also implies that the set of rigid parameters is not closed in the moduli space of cubic polynomials.