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An endomorphism of a finitely generated free group naturally descends to an injective endomorphism on the stable quotient. We establish a geometric incarnation of this fact : an expanding irreducible train track map inducing an endomorphism of the fundamental group determines an expanding irreducible train track representative of the injective endomorphism of the stable quotient. As an application, we prove that the property of having fully irreducible monodromy for a splitting of a hyperbolic free-by-cyclic group G depends only on the component of the BNS invariant $\sum \left ( G \right )$ containing the associated homomorphism to the integers. In particular, it follows that if G is the mapping torus of an atoroidal fully irreducible automorphism of a free group and if the union of $\sum \left ( G \right ) $ and $\sum \left ( G \right )$ is connected then for every splitting of $G$ as a (f.g. free)-by-(infinite cyclic) group the monodromy is fully irreducible.
This talk is based on joint work with Spencer Dowdall and Christopher Leininger. An endomorphism of a finitely generated free group naturally descends to an injective endomorphism on the stable quotient. We establish a geometric incarnation of this fact : an expanding irreducible train track map inducing an endomorphism of the fundamental group determines an expanding irreducible train track representative of the injective endomorphism of the stable quotient. As an application, we prove that the property of having fully ...

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Documents 37Bxx | enregistrements trouvés : 26

Endomorphisms, train track maps, and fully irreducible monodromies Kapovich, Ilya | CIRM H Nouveau

Emergence of wandering stable components Berger, Pierre | CIRM H Nouveau

Operator Structures and Dynamical Systems :Satellite Conference of the Fifth European Congress of Mathematics Leiden # July, 21-25, 2008, Jeu, Marcel de ; Silvestrov, Sergei ; Skau, Christian ; Tomiyama, Jun | American Mathematical Society 2009 Nouveau

Asymptotic geometric analysis:proceedings of the fall 2010 Fields institute thematic program Ludwig, Monika ; Milman, Vitali D. ; Pestov, Vladimir ; Tomczak-Jaegermann, Nicole | Springer;The Fields Institute for Research in Mathematical Sciences 2013 Nouveau

Dynamical systems and random processes:16th Carolina dynamics symposiumDecatur # April 13-15, 2018 Hawkins, Jane ; Rossetti, Rachel L. ; Wiseman, Jim | American Mathematical Society 2019 Nouveau

Dynamics: topology and numbers.ConferenceBonn # July 2-6, 2018 Moree, Pieter ; Pohl, Anke ; Snoha, L'ubomír ; Ward, Tom | American Mathematical Society 2020 Nouveau

Symbolic dynamics : one-sided, two-sided and countable state Markov shifts Kitchens, Bruce P. | Springer 1998 Nouveau

An introduction to symbolic dynamics and coding Lind, Douglas ; Marcus, Brian | Cambridge University Press 1995 Nouveau

Volterra integral equations and topological dynamics Miller, Richard K. ; Sell, George R. | American Mathematical Society 1970 Nouveau

Substitutions in dynamics, arithmetics and combinatorics Pytheas Fogg, N. ; Berthé, V. ; Ferenczi, S. ; Mauduit, Christian ; Siegel, A. | Springer 2002 Nouveau

Topological invariants for projection method patterns Forrest, Alan ; Hunton, John ; Kellendonk, Johannes | American Mathematical Society 2002 Nouveau

Topics in dynamics and ergodic theory Bezuglyi, Sergey ; Kolyada, Sergiy | Cambridge University Press 2003 Nouveau

Ergodic theory via joinings Glasner, Eli | American Mathematical Society 2003 Nouveau

Topics from one-dimensional dynamics Brucks, Karen M. ; Bruin, Henk | Cambridge University Press 2004 Nouveau

Gradient inequalities :with applications to asymptotic behavior and stability of gradient-like systems Huang, Sen-Zhong | American Mathematical Society 2006 Nouveau

Dynamical systems, graphs, and algorithms Osipenko, G. | Springer 2006 Nouveau

Topology of tiling spaces Sadun, Lorenzo | American Mathematical Society 2008 Nouveau

Dynamical systems and group actions. Bowen, Lewis ; Grigorchuk, Rostislav ; Vorobets, Yaroslav | American Mathematical Society 2012 Nouveau

Dynamical systems:an introduction Barreira, Luis ; Valls, Claudia | Springer 2013 Nouveau

Introduction to dynamical systems Brin, Michael ; Stuck, Garrett | Cambridge University Press 2015 Nouveau

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Operator Structures and Dynamical Systems :
Satellite Conference of the Fifth European Congress of Mathematics
Leiden # July, 21-25, 2008, Jeu, Marcel de ; Silvestrov, Sergei ; Skau, Christian ; Tomiyama, Jun | American Mathematical Society 2009 Nouveau

Asymptotic geometric analysis:
proceedings of the fall 2010 Fields institute thematic program Ludwig, Monika ; Milman, Vitali D. ; Pestov, Vladimir ; Tomczak-Jaegermann, Nicole | Springer;The Fields Institute for Research in Mathematical Sciences 2013 Nouveau

Dynamical systems and random processes:
16th Carolina dynamics symposium
Decatur # April 13-15, 2018 Hawkins, Jane ; Rossetti, Rachel L. ; Wiseman, Jim | American Mathematical Society 2019 Nouveau

Dynamics: topology and numbers.
Conference
Bonn # July 2-6, 2018 Moree, Pieter ; Pohl, Anke ; Snoha, L'ubomír ; Ward, Tom | American Mathematical Society 2020 Nouveau

Symbolic dynamics :
one-sided, two-sided and countable state Markov shifts Kitchens, Bruce P. | Springer 1998 Nouveau

Gradient inequalities :
with applications to asymptotic behavior and stability of gradient-like systems Huang, Sen-Zhong | American Mathematical Society 2006 Nouveau

Dynamical systems:
an introduction Barreira, Luis ; Valls, Claudia | Springer 2013 Nouveau