APPM Comprehensive Exam - Amanda Hampton

Amanda Hampton, Department of Applied Mathematics, University of Colorado Boulder

Aubry and Abramovici’s concept of anti-integrability (AI) was first described thirty years ago [AA90] for discrete-time Hamiltonian systems as a complementary idea to integrability. Generally, anti-integrable systems are strongly perturbed integrable systems that result in fully chaotic dynamics. Most work in AI has been with discrete Lagrangian systems and 2n-dimensional symplectic maps, with results regarding the existence and persistence of certain structural behaviors, such as the existence of cantori under particular rotational conditions. There are many open questions when addressing more general maps and the development of structural behavior over a large parameter range.

This document serves as a brief discussion on the proposed project of anti-integrability for 3D quadratic maps. We describe the concept of anti-integrability and its origins in §2 and understand how AI can be applied to a generic quadratic 3D map in §3. In §4, we summarize preliminary results, submitted for review [HM], detailing work for one particular AI limit and creating a foundation for our intended methodology as we progress these ideas further. Lastly, in §5 we list different directions this project could take.

Passcode for this talk is NotThatAI!

 

Dial-In Information

https://cuboulder.zoom.us/j/92371672295; passcode NotThatAI!

Tuesday, November 16, 2021 at 2:00pm to 4:00pm

Virtual Event
Event Type

Colloquium/Seminar

Interests

Science & Technology, Research & Innovation

Audience

Faculty

College, School & Unit

Engineering & Applied Science

Tags

Comprehensive Exam

Group
Applied Mathematics
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