Displaying similar documents to “Homogenization of codimension 1 actions of n near a compact orbit”

Topological friction in aperiodic minimal m -actions

Jarosław Kwapisz (2010)

Fundamenta Mathematicae

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For a continuous map f preserving orbits of an aperiodic m -action on a compact space, its displacement function assigns to x the “time” t m it takes to move x to f(x). We show that this function is continuous if the action is minimal. In particular, f is homotopic to the identity along the orbits of the action.

Non-orbit equivalent actions of 𝔽 n

Adrian Ioana (2009)

Annales scientifiques de l'École Normale Supérieure

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For any 2 n , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group 𝔽 n . These actions arise as diagonal products between a generalized Bernoulli action and the action 𝔽 n ( 𝕋 2 , λ 2 ) , where 𝔽 n is seen as a subgroup of SL 2 ( ) .

A map maintaining the orbits of a given d -action

Bartosz Frej, Agata Kwaśnicka (2016)

Colloquium Mathematicae

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Giordano et al. (2010) showed that every minimal free d -action of a Cantor space X is orbit equivalent to some ℤ-action. Trying to avoid the K-theory used there and modifying Forrest’s (2000) construction of a Bratteli diagram, we show how to define a (one-dimensional) continuous and injective map F on X∖one point such that for a residual subset of X the orbits of F are the same as the orbits of a given minimal free d -action.

Shadowing in multi-dimensional shift spaces

Piotr Oprocha (2008)

Colloquium Mathematicae

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We show that the class of expansive d actions with P.O.T.P. is wider than the class of actions topologically hyperbolic in some direction ν d . Our main tool is an extension of a result by Walters to the multi-dimensional symbolic dynamics case.

Finite actions on the Klein four-orbifold and prism manifolds

John Kalliongis, Ryo Ohashi (2017)

Commentationes Mathematicae Universitatis Carolinae

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We describe the finite group actions, up to equivalence, which can act on the orbifold Σ ( 2 , 2 , 2 ) , and their quotient types. This is then used to consider actions on prism manifolds M ( b , d ) which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If ϕ : G Homeo ( M ( b , d ) ) is such an action, we show that M ( b , d ) = M ( b , 2 ) and M ( b , 2 ) / ϕ fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by Σ ( 2 , 2 , 2 ) . For the standard actions, we compute the fundamental group of M ( b , 2 ) / ϕ and...

On finite groups acting on a connected sum of 3-manifolds S² × S¹

Bruno P. Zimmermann (2014)

Fundamenta Mathematicae

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Let H g denote the closed 3-manifold obtained as the connected sum of g copies of S² × S¹, with free fundamental group of rank g. We prove that, for a finite group G acting on H g which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but there does not exist a linear bound in g. This implies then a Jordan-type bound for arbitrary finite group actions on H g which is quadratic in g. For the proofs we develop a calculus...

Shadowing in actions of some Abelian groups

Sergei Yu. Pilyugin, Sergei B. Tikhomirov (2003)

Fundamenta Mathematicae

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We study shadowing properties of continuous actions of the groups p and p × p . Necessary and sufficient conditions are given under which a linear action of p on m has a Lipschitz shadowing property.

Oscillation conditions for difference equations with several variable arguments

George E. Chatzarakis, Takaŝi Kusano, Ioannis P. Stavroulakis (2015)

Mathematica Bohemica

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Consider the difference equation Δ x ( n ) + i = 1 m p i ( n ) x ( τ i ( n ) ) = 0 , n 0 x ( n ) - i = 1 m p i ( n ) x ( σ i ( n ) ) = 0 , n 1 , where ( p i ( n ) ) , 1 i m are sequences of nonnegative real numbers, τ i ( n ) [ σ i ( n ) ], 1 i m are general retarded (advanced) arguments and Δ [ ] denotes the forward (backward) difference operator Δ x ( n ) = x ( n + 1 ) - x ( n ) [ x ( n ) = x ( n ) - x ( n - 1 ) ]. New oscillation criteria are established when the well-known oscillation conditions lim sup n i = 1 m j = τ ( n ) n p i ( j ) > 1 lim sup n i = 1 m j = n σ ( n ) p i ( j ) > 1 and lim inf n i = 1 m j = τ i ( n ) n - 1 p i ( j ) > 1 e lim inf n i = 1 m j = n + 1 σ i ( n ) p i ( j ) > 1 e are not satisfied. Here τ ( n ) = max 1 i m τ i ( n ) [ σ ( n ) = min 1 i m σ i ( n ) ] . The results obtained essentially improve known results in the literature. Examples illustrating the results are also given.

Correction for the paper “ S 3 -bundles and exotic actions”

T. E. Barros (2001)

Bulletin de la Société Mathématique de France

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In [R] explicit representatives for S 3 -principal bundles over S 7 are constructed, based on these constructions explicit free S 3 -actions on the total spaces are described, with quotients exotic 7 -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic 7 -spheres that occur as quotients of the free S 3 -actions described...

Explicit computations of all finite index bimodules for a family of II 1 factors

Stefaan Vaes (2008)

Annales scientifiques de l'École Normale Supérieure

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We study II 1 factors M and N associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index M - N -bimodule (in particular, every isomorphism between M and N ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index M - M -bimodules is identified with an extended Hecke fusion algebra,...

On the stratification of the orbit space for the action of automorphisms on connections

Witold Kondracki, Jan Rogulski

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CONTENTSIntroduction..................................................................................................................................................5§1. Basic notions and notation.....................................................................................................................7  1.1. Automorphisms of principal bundles....................................................................................................7  1.2. Connections and parallel...

Z k -actions with a special fixed point set

Pedro L. Q. Pergher, Rogério de Oliveira (2005)

Fundamenta Mathematicae

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Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if N m is any smooth and closed m-dimensional manifold with m > n and T : N m N m is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions ( M m ; Φ ) of the group G = Z k on closed smooth m-dimensional manifolds M m for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....

Z k -actions fixing point ∪ Vⁿ

Pedro L. Q. Pergher (2002)

Fundamenta Mathematicae

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We describe the equivariant cobordism classification of smooth actions ( M m , Φ ) of the group G = Z k on closed smooth m-dimensional manifolds M m for which the fixed point set of the action is the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally,...

Extensions of generic measure-preserving actions

Julien Melleray (2014)

Annales de l’institut Fourier

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We show that, whenever Γ is a countable abelian group and Δ is a finitely-generated subgroup of Γ , a generic measure-preserving action of Δ on a standard atomless probability space ( X , μ ) extends to a free measure-preserving action of Γ on ( X , μ ) . This extends a result of Ageev, corresponding to the case when Δ is infinite cyclic.

Diagonal points having dense orbit

T. K. Subrahmonian Moothathu (2010)

Colloquium Mathematicae

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Let f: X→ X be a topologically transitive continuous map of a compact metric space X. We investigate whether f can have the following stronger properties: (i) for each m ∈ ℕ, f × f ² × × f m : X m X m is transitive, (ii) for each m ∈ ℕ, there exists x ∈ X such that the diagonal m-tuple (x,x,...,x) has a dense orbit in X m under the action of f × f ² × × f m . We show that (i), (ii) and weak mixing are equivalent for minimal homeomorphisms, that all mixing interval maps satisfy (ii), and that there are mixing subshifts not satisfying...

Relative exactness modulo a polynomial map and algebraic ( p , + ) -actions

Philippe Bonnet (2003)

Bulletin de la Société Mathématique de France

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Let F = ( f 1 , ... , f q ) be a polynomial dominating map from n to  q . We study the quotient 𝒯 1 ( F ) of polynomial 1-forms that are exact along the generic fibres of F , by 1-forms of type d R + a i d f i , where R , a 1 , ... , a q are polynomials. We prove that 𝒯 1 ( F ) is always a torsion [ t 1 , ... , t q ] -module. Then we determine under which conditions on F we have 𝒯 1 ( F ) = 0 . As an application, we study the behaviour of a class of algebraic ( p , + ) -actions on n , and determine in particular when these actions are trivial.

Minimal models for d -actions

Bartosz Frej, Agata Kwaśnicka (2008)

Colloquium Mathematicae

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We prove that on a metrizable, compact, zero-dimensional space every d -action with no periodic points is measurably isomorphic to a minimal d -action with the same, i.e. affinely homeomorphic, simplex of measures.