| Abstract: |
| Recently, some fruitful approaches were found to express complexity of Hamiltonian or Reeb dynamics in terms of Floer theory or contact homology. One goes back to Alves and Pirnapasov, where the growth of essential homotopy classes of orbits in a complement of a link of periodic orbits in 3-dimensional flows is studied, another is due to Cineli, Ginzburg, and Gurel, through the study of barcode entropy.
In my talk, I will explain some recent results on estimates of the barcode entropy of Hamiltonian diffeomorphisms relative to pairs of Lagrangian submanifolds, and discuss connections to other properties of the dynamics. Some of the results reveal moreover some interesting connections between the two approaches to complexity mentioned above. |
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