Rigidity theorems showing conjugacy from matching or diagonalizable periodic orbit stabilizers for time changes of Anosov flow products, with 3-manifold equivalences and conjecture counterexamples.
En- cyclopedia of Mathematics and its Applications, vol
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Under a domination condition, real-analytic deformations of symplectomorphism products yield large robustly transitive sets and new non-uniformly-hyperbolic examples via blender-horseshoe perturbations and control-theory ideas.
Proves the conditional minimal-intermediate-entropy property holds for topologically expanding maps, transitive countable Markov shifts, and symbolic systems with non-uniform structure via adapted multi-horseshoe constructions.
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Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.
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Rigidity phenomena for time changes of products of Anosov flows
Rigidity theorems showing conjugacy from matching or diagonalizable periodic orbit stabilizers for time changes of Anosov flow products, with 3-manifold equivalences and conjecture counterexamples.
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Under a domination condition, real-analytic deformations of symplectomorphism products yield large robustly transitive sets and new non-uniformly-hyperbolic examples via blender-horseshoe perturbations and control-theory ideas.
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Proves the conditional minimal-intermediate-entropy property holds for topologically expanding maps, transitive countable Markov shifts, and symbolic systems with non-uniform structure via adapted multi-horseshoe constructions.
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Proves local centralizer rigidity results for elements of Weyl chamber flows and twisted Weyl chamber flows on compact homogeneous spaces.
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Isomoprhism of generalized Bratteli diagrams
Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.