International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps

Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable, volume-preserving maps with one action and $d$ angles. For the area-preserving case, Greene's residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. We study a three-dimensional, reversible, volume-preserving analogue of Chirikov's standard map with one action and two angles. We investigate the preservation and destruction of tori under perturbation by computing the "residue" of nearby periodic orbits. We find tori with Diophantine rotation vectors in the "spiral mean" cubic algebraic field. The residue is used to generate the critical function of the map and find a candidate for the most robust torus.Comment: laTeX, 40 pages, 26 figure