We introduce a new decomposition of Weinstein 4-manifolds called multisections with divides and show these can be encoded diagrammatically by a sequence of cut systems on a surface, together with a separating collection of curves. We give two algorithms to construct a multisection with divides for a Weinstein 4-manifold, one starting with a Kirby-Weinstein handle decomposition and the other starting with a positive, allowable Lefschetz fibration (PALF). Through the connections with PALFs, we define a monodromy of a multisection and show how to symplectically carry out monodromy substitution on multisections with divides.
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Strongly mixing smooth planar vector field without asymptotic directions
Abstract We use a Voronoi-type tessellation based on a compound Poisson point process to construct a polynomially mixing stationary random smooth planar vector field with bounded nonnegative components such that, with probability one, none of the associated integral curves possess an asymptotic direction.
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- Award ID(s):
- 1811444
- PAR ID:
- 10428428
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 36
- Issue:
- 3
- ISSN:
- 0951-7715
- Page Range / eLocation ID:
- 1789 to 1798
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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