Computer-aided proofs for non-hyperbolic dynamics and blenders

非双曲动力学和混合器的计算机辅助证明

• 批准号: DP220100492
• 负责人: Prof Warwick Tucker
• 金额: $ 28.81万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220100492
• 关键词: Computer; aided; proofs; non; hyperbolic

This project aims to develop methods to rigorously detect certain geometric structures in systems that are known to imply chaos and are robust under perturbation. Such structures include blenders and robust heterodimensional cycles and homoclinic tangencies. This project expects to generate new knowledge in the area of non hyperbolic dynamics utilising a novel combination of recent developments in Dynamical Systems and techniques from rigorous numerics. Expected outcomes of this project include an efficient computation platform aimed at detecting and verifying chaos-inducing objects in complex dynamical systems. This should provide significant benefits, such as an increased understanding of non-hyperbolic dynamical systems.

该项目旨在开发方法来严格检测系统中的某些几何结构，这些结构已知隐含混沌并且在扰动下具有鲁棒性。这样的结构包括混合体、坚固的异维循环和同斜切线。