Authors define an Entropy flow on phase-parameter space that augments one-parameter vector field families with a parameter drift to realize transitions to chaos, and examine its behavior on standard routes and example systems.
A beginner's introduction to Fukaya categories
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abstract
The goal of these notes is to give a short introduction to Fukaya categories and some of their applications. The first half of the text is devoted to a brief review of Lagrangian Floer (co)homology and product structures. Then we introduce the Fukaya category (informally and without a lot of the necessary technical detail), and briefly discuss algebraic concepts such as exact triangles and generators. Finally, we mention wrapped Fukaya categories and outline a few applications to symplectic topology, mirror symmetry and low-dimensional topology. This text is based on a series of lectures given at a Summer School on Contact and Symplectic Topology at Universit\'e de Nantes in June 2011.
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UNVERDICTED 2representative citing papers
A new Floer homology theory is built with chain complex generated by isosceles trapezoid inscriptions, proving their existence on every smooth Jordan curve and on new classes of non-smooth ones via action filtration spectral invariants.
citing papers explorer
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When Entropy flows: drifting along the route to Chaos
Authors define an Entropy flow on phase-parameter space that augments one-parameter vector field families with a parameter drift to realize transitions to chaos, and examine its behavior on standard routes and example systems.
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Inscriptions of Isosceles Trapezoids in Jordan Curves
A new Floer homology theory is built with chain complex generated by isosceles trapezoid inscriptions, proving their existence on every smooth Jordan curve and on new classes of non-smooth ones via action filtration spectral invariants.