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On the S-Euclidean minimum of an ideal class

Kevin J. McGown (2015)

Acta Arithmetica

We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from...

On the ω-limit sets of tent maps

Andrew D. Barwell, Gareth Davies, Chris Good (2012)

Fundamenta Mathematicae

For a continuous map f on a compact metric space (X,d), a set D ⊂ X is internally chain transitive if for every x,y ∈ D and every δ > 0 there is a sequence of points ⟨x = x₀,x₁,...,xₙ = y⟩ such that d ( f ( x i ) , x i + 1 ) < δ for 0 ≤ i< n. In this paper, we prove that for tent maps with periodic critical point, every closed, internally chain transitive set is necessarily an ω-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed,...

On time reparametrizations and isomorphisms of impulsive dynamical systems

Krzysztof Ciesielski (2004)

Annales Polonici Mathematici

We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined for all positive times. We also prove that for a given impulsive system it is possible to change the topology in the phase space so that we may consider the system as a semidynamical system (without impulses).

On top spaces.

Molaei, M.R., Khadekar, G.S., Farhangdost, M.R. (2006)

Balkan Journal of Geometry and its Applications (BJGA)

On two recurrence problems

Michael Boshernitzan, Eli Glasner (2009)

Fundamenta Mathematicae

We review some aspects of recurrence in topological dynamics and focus on two open problems. The first is an old one concerning the relation between Poincaré and Birkhoff recurrence; the second, due to the first author, is about moving recurrence. We provide a partial answer to a topological version of the moving recurrence problem.

Orbit coupling

Hans-Otto Georgii (1997)

Annales de l'I.H.P. Probabilités et statistiques

Orbit equivalence and Kakutani equivalence with Sturmian subshifts

P. Dartnell, F. Durand, A. Maass (2000)

Studia Mathematica

Using dimension group tools and Bratteli-Vershik representations of minimal Cantor systems we prove that a minimal Cantor system and a Sturmian subshift are topologically conjugate if and only if they are orbit equivalent and Kakutani equivalent.

Ordered K-theoryand minimal symbolic dynamical systems

Christian Skau (2000)

Colloquium Mathematicae

Recently a new invariant of K-theoretic nature has emerged which is potentially very useful for the study of symbolic systems. We give an outline of the theory behind this invariant. Then we demonstrate the relevance and power of the invariant, focusing on the families of substitution minimal systems and Toeplitz flows.

Periods and entropy for Lorenz-like maps

Lluis Alsedà, J. Llibre, M. Misiurewicz, C. Tresser (1989)

Annales de l'institut Fourier

We characterize the set of periods and its structure for the Lorenz-like maps depending on the rotation interval. Also, for these maps we give the best lower bound of the topological entropy as a function of the rotation interval.

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