50 citations · 183 across the 26 of their papers we have counts for
29 papers
Ergodicity Of Partially Hyperbolic Endomorphisms
Andy Hammerlindl, Audrey Tyler
We prove that for volume preserving, partially hyperbolic, center bunched endomorphisms with constant Jacobian, essential accessibility implies ergodicity.
Horizontality of partially hyperbolic foliations
Andy Hammerlindl, Rafael Potrie
We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic s…
Bundle switching in higher dimensions
Andy Hammerlindl
Assuming it preserves an orientation of its stable bundle, any three-dimensional partially hyperbolic diffeomorphism can be used to construct a four-dimensional partially hyperboli…
Nowhere coexpanding functions
Andrew Cook, Andy Hammerlindl, Warwick Tucker
We define a family of functions which we call "nowhere coexpanding functions" that is closed under composition and includes all functions with non-positive Schwarzian d…
Classification of partially hyperbolic surface endomorphisms
Layne Hall, Andy Hammerlindl
We show that in the absence of periodic centre annuli, a partially hyperbolic surface endomorphism is dynamically coherent and leaf conjugate to its linearisation. We proceed to ch…
Dynamically incoherent surface endomorphisms
Layne Hall, Andy Hammerlindl
We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of in the homotopy class of any linear expanding map with integer eigenvalues. Th…
Quantitative global-local mixing for accessible skew products
P. Giulietti, A. Hammerlindl, D. Ravotti
We study global-local mixing for a family of accessible skew products with an exponentially mixing base and non-compact fibers, preserving an infinite measure. For a dense set of a…
Accessibility of derived-from-Anosov systems
Andy Hammerlindl, Yi Shi
This paper shows any non-Anosov partially hyperbolic diffeomorphism on the 3-torus which is homotopic to Anosov must be accessible.
Ergodicity and partial hyperbolicity on Seifert manifolds
Andy Hammerlindl, Jana Rodriguez Hertz, Raul Ures
We show that conservative partially hyperbolic diffeomorphism isotopic to the identity on Seifert 3-manifolds are ergodic.
Global manifold structure of a continuous-time heterodimensional cycle
Andy Hammerlindl, Bernd Krauskopf, Gemma Mason +1
A heterodimensional cycle consists of a pair of heteroclinic connections between two saddle periodic orbits with unstable manifolds of different dimensions. Recent theoretical work…
Partially hyperbolic surface endomorphisms
Layne Hall, Andy Hammerlindl
We prove that a class of weakly partially hyperbolic endomorphisms on are dynamically coherent and leaf conjugate to linear toral endomorphisms. Moreover, we give an…
Horizontal vector fields and Seifert fiberings
Andy Hammerlindl
This paper gives a classification of the topology of vector fields which are nowhere tangent to the fibers of a Seifert fibering.
Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence
Christian Bonatti, Andrey Gogolev, Andy Hammerlindl +1
Let be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M…
Classification of systems with center-stable tori
Andy Hammerlindl, Rafael Potrie
This paper gives a classification of partially hyperbolic systems in dimension 3 which have at least one torus tangent to the center-stable bundle.
Seifert manifolds admitting partially hyperbolic diffeomorphisms
Andy Hammerlindl, Rafael Potrie, Mario Shannon
We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a tra…
Properties of compact center-stable submanifolds
Andy Hammerlindl
We show that a partially hyperbolic system can have at most a finite number of compact center-stable submanifolds. We also give sufficient conditions for these submanifolds to exis…
Constructing center-stable tori
Andy Hammerlindl
We show that any weakly partially hyperbolic diffeomorphism on the 2-torus may be realized as the dynamics on a center-stable or center-unstable torus of a 3-dimensional strongly p…
Partial hyperbolicity and classification: a survey
Andy Hammerlindl, Rafael Potrie
This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensio…
A trajectory-free framework for analysing multiscale systems
Gary Froyland, Georg A. Gottwald, Andy Hammerlindl
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate…
Center bunching without dynamical coherence
Andy Hammerlindl
We answer a question of Burns and Wilkinson, showing that there are open families of volume-preserving partially hyperbolic diffeomorphisms which are accessible and center bunched…
Ergodic components of partially hyperbolic systems
Andy Hammerlindl
This paper gives a complete classification of the possible ergodic decompositions for certain open families of volume-preserving partially hyperbolic diffeomorphisms. These familie…
A computational method to extract macroscopic variables and their dynamics in multiscale systems
Gary Froyland, Georg A. Gottwald, Andy Hammerlindl
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In partic…
Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group
Andy Hammerlindl, Rafael Potrie
A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit…
On expanding foliations
Andy Hammerlindl
Certain families of manifolds which support Anosov flows do not support expanding, quasi-isometric foliations.