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Transitivity of conservative toral endomorphisms

Martin Andersson
2016 Nonlinearity  
It is shown that if a non-invertible area preserving local homeomorphism on T^2 is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive.  ...  This gives a complete characterization, in any smoothness category, of those homotopy classes of conservative endomorphisms that consist entirely of transitive maps.  ...  The existence of non-trivial strictly invariant regular open sets is independent of whether the endomorphism is invertible or not.  ... 
doi:10.1088/0951-7715/29/3/1047 fatcat:3ud6sjjkpvbj3mxwvomzutggyu

Transitive endomorphisms with critical points [article]

Wagner Ranter
2017 arXiv   pre-print
We show that a non-wandering endomorphism of the torus with invertible linear part without invariant directions and for which the critical points are in some sense generic is transitive.  ...  Acknowledgments The author 3 would like to express his gratitude to Professor Enrique Pujals and to Rafael Potrie, as well as to Professor Cristina Lizana for their helpful comments and appropriate advices  ...  Then the following are equivalent: (i) W is essential; (ii) W contains a loop homotopically non-trivial in T 2 ; (iii) there is a non-trivial deck transformation T w : R 2 → R 2 such that every connected  ... 
arXiv:1608.06921v2 fatcat:uftlshwsejg43ocp4cwibf25ne

Morphisms for Non-trivial Non-linear Invariant Generation for Algebraic Hybrid Systems [chapter]

Nadir Matringe, Arnaldo Vieira Moura, Rachid Rebiha
2009 Lecture Notes in Computer Science  
The non-trivial non-linear invariant generation problem is then reduced to linear algebraic problems associated to the identified endomorphisms.  ...  is known that lends itself to non-trivial non-linear invariants generation.  ... 
doi:10.1007/978-3-642-00602-9_32 fatcat:5xm25sfn5vcsncryorheyfwlcm

K-theoretic torsion and the zeta function [article]

John R. Klein, Cary Malkiewich
2020 arXiv   pre-print
We also exhibit several examples of families of endomorphisms having non-trivial endomorphism torsion.  ...  Our identity involves a higher torsion invariant, the endomorphism torsion, of a parametrized family of endomorphisms as well as a higher zeta function of such a family.  ...  By Proposition 3.3, we infer that the loop (15) is non-trivial, and conclude the following. Theorem 8.5. The endomorphism torsion invariant of the above pair (p, f ) is non-trivial in K 2 (Q(t)).  ... 
arXiv:2009.10120v1 fatcat:gjnvq4v54rg5fbl5y4rsxrtany

Modular invariants from subfactors [article]

J. Böckenhauer, D. E. Evans
2000 arXiv   pre-print
Several properties of modular invariants have so far been noticed empirically and considered mysterious such as their intimate relationship to graphs, as for example the A-D-E classification for SU(2)_  ...  Moreover the fusion rule isomorphism for maximally extended chiral algebras due to Moore-Seiberg, Dijkgraaf-Verlinde finds a clear and very general proof and interpretation through intermediate subfactors  ...  Zuber for helpful comments on an earlier version of the manuscript.  ... 
arXiv:math/0006114v2 fatcat:waaq3lhexzapzn6k33yclw3n4m

FUSION RULES OF MODULAR INVARIANTS

DAVID E. EVANS
2002 Reviews in Mathematical Physics  
The decomposition of the non-normalized modular invariants Z Z^* and Z^*Z into sums of normalized modular invariants is related to the decomposition of the full induced M-M system of sectors.  ...  Modular invariants satisfy remarkable fusion rules. Let Z be a modular invariant associated to a braided subfactor N⊂ M.  ...  I am grateful for the organizers and MSRI for their invitation and financial support.  ... 
doi:10.1142/s0129055x02001351 fatcat:slm7yvubufbdvo7y4dcciz2664

Strongly irreducible operators and indecomposable representations of quivers on infinite-dimensional Hilbert spaces [article]

Masatoshi Enomoto, Yasuo Watatani
2013 arXiv   pre-print
We shall show two kinds of constructions of quite non-trivial indecomposable Hilbert representations of the Kronecker quiver such that their endomorphism rings are trivial, which are called transitive.  ...  there exist no non-trivial invariant (closed) subspaces M and N of T such that M ∩ N = 0 and M + N = H.  ...  In fact this is the invariant subspace problem, that is, the question whether any operator A on H has a non-trivial (closed) invariant subspace. Definition.  ... 
arXiv:1303.2485v1 fatcat:nqlzsc5pjvguhohi2eckum6peu

Page 8064 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
This matrix Z is in many instances a modular invariant. For instance, in the case of Wassermann’s SU(N) loop group subfactors Z is a modular invariant for the SU(N), Wess-Zumino-Witten models.  ...  The methods of proof are applied to the reduced general linear group GL*,(/;(A)) for C*-subalgebras A of the C*-algebra of compact operators on /; and for C*-algebras A = Co(M) for finite-dimensional manifolds  ... 

Subfactors and coset models [article]

K.-H. Rehren
1993 arXiv   pre-print
It is reducible iff the relative commutant σ(M) ′ ∩ M is non-trivial. Every projection e ∈ σ(M) ′ ∩ M corresponds to a sub-endomorphism σ e defined as follows.  ...  Discussion and outlook We have seen that some non-trivial sectors of a subtheory H l ⊗ W and a forteriori of H l alone are in fact generated by local fields of the theory G k .  ...  Next, (2.2(i)) yields for every k, implying the linear transformation law (2.15) for ψ ∝ φ.  ... 
arXiv:hep-th/9308145v1 fatcat:p22iltlulfdgxkdpnrdiju5lre

Topology of Fatou components for endomorphisms of CPk: linking with the Green's current

Suzanne Lynch Hruska, Roland K. W. Roeder
2010 Fundamenta Mathematicae  
It has the property that if lk(γ, S) = 0, then γ represents a non-trivial homology element in H1(CP k \ supp S).  ...  For example, we prove that the Fatou set has infinitely generated first homology for any polynomial endomorphism of CP 2 for which the restriction to the line at infinity is hyperbolic and has disconnected  ...  Hubbard for bringing us and some central ideas together at the start of this project.  ... 
doi:10.4064/fm210-1-4 fatcat:xf62rf3bnzg3tkigs2w2accn7e

Topology of Fatou components for endomorphisms of CP^k: Linking with the Green's Current [article]

Suzanne Lynch Hruska, Roland K.W. Roeder
2010 arXiv   pre-print
It has the property that if lk(γ,S) ≠ 0, then γ represents a non-trivial homology element in H_1(CP^k ∖ S).  ...  For example, we prove that the Fatou set has infinitely generated first homology for any polynomial endomorphism of CP^2 for which the restriction to the line at infinity is hyperbolic and has disconnected  ...  Hubbard for bringing us and some central ideas together at the start of this project.  ... 
arXiv:0810.1673v3 fatcat:6t7qmxpbu5duhlckm2kjxkrkza

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

Maximilian Demmel, Frank Saueressig, Omar Zanusso
2015 Annals of Physics  
The geometric flow reproduces the phase-diagram of the Einstein-Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety.  ...  We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields.  ...  Reuter for many helpful discussions. The research of F. S. and O. Z. has been supported by the Deutsche Forschungsgemeinschaft (DFG) within the Emmy-Noether program (Grant SA/1975 1-1).  ... 
doi:10.1016/j.aop.2015.04.018 fatcat:yrkqrqthfrdl7lk7lrqx2ebdti

RG flows of Quantum Einstein Gravity in the linear-geometric approximation [article]

Maximilian Demmel, Frank Saueressig, Omar Zanusso
2015 arXiv   pre-print
The geometric flow reproduces the phase-diagram of the Einstein-Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety.  ...  We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields.  ...  Reuter for many helpful discussions. The research of F. S. and O. Z. has been supported by the Deutsche Forschungsgemeinschaft (DFG) within the Emmy-Noether program (Grant SA/1975 1-1).  ... 
arXiv:1412.7207v2 fatcat:n7lnokgjszcdnghkia74tecofi

Endomorphisms of graph algebras [article]

Roberto Conti, Jeong Hee Hong, Wojciech Szymanski
2012 arXiv   pre-print
In particular, criteria of outerness for automorphisms in the restricted Weyl group are found.  ...  of permutative endomorphisms.  ...  We are grateful to the referee for very careful reading of the manuscript and a number of comments which helped to improve the presentation.  ... 
arXiv:1101.4210v3 fatcat:iabclg7fyjd5nodgtdhonzww2y

A remark on the Reeb flow for spheres

Roger Casals, Francisco Presas
2014 The Journal of Symplectic Geometry  
The class in π 1 (Cont(S 2n+1 , ξ 0 )) generated by the Reeb flow of α 0 is a non-trivial element for n = 3. R. Casals and F. Presas Preliminaries Contact structures Definition 3.  ...  See [El] for the 3-sphere and [Bo, Ge] for torus bundles. In the present note we prove the non-triviality of its second homotopy group for 3-Sasakian manifolds, see [BG].  ...  The class in π 1 (Cont(S 4n+3 , ξ 0 )) generated by the Reeb flow of α 0 is a non-trivial element of infinite order for n = 1.  ... 
doi:10.4310/jsg.2014.v12.n4.a1 fatcat:hrvskekbsja53fptusqwj7so7q
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