Search results for "Invariant"
showing 10 items of 783 documents
Forbidden words in symbolic dynamics
2000
AbstractWe introduce an equivalence relation≃between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the≃-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of sofic systems, we prove that the≃-equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having “different slope” are not conjugate.
On the existence of conditionally invariant probability measures in dynamical systems
2000
Let T : X→X be a measurable map defined on a Polish space X and let Y be a non-trivial subset of X. We give conditions ensuring the existence of conditionally invariant probability measures to non-absorption in Y. For dynamics which are non-singular with respect to some fixed probability measure we supply sufficient conditions for the existence of absolutely continuous conditionally invariant measures. These conditions are satisfied for a wide class of dynamical systems including systems that are Φ-mixing and Gibbs.
Invariant characters and coprime actions on finite nilpotent groups
2000
Suppose that a group A acts via automorphisms on a nilpotent group G having coprime order. Given an A-invariant character \(\chi \in {\rm Irr}(G)\), we show that the A-primitive irreducible characters that induce \(\chi \) from an A-invariant subgroup of G all have equal degree. We use this result to obtain some information about the characters of groups of p-length 1.
Topological invariants of stable immersions of oriented 3-manifolds in R4
2012
Abstract We show that the Z -module of first order local Vassiliev type invariants of stable immersions of oriented 3-manifolds into R 4 is generated by 3 topological invariants: The number of pairs of quadruple points and the positive and negative linking invariants l + and l − introduced by V. Goryunov (1997) [7] . We obtain the expression for the Euler characteristic of the immersed 3-manifold in terms of these invariants. We also prove that the total number of connected components of the triple points curve is a non-local Vassiliev type invariant.
Coupled fixed point, F-invariant set and fixed point of N-order
2010
In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of $F$-invariant set. We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement some known existence results from the literature.
Defining relations of minimal degree of the trace algebra of 3×3 matrices
2008
Abstract The trace algebra C n d over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n , d ⩾ 2 . Minimal sets of generators of C n d are known for n = 2 and n = 3 for any d as well as for n = 4 and n = 5 and d = 2 . The defining relations between the generators are found for n = 2 and any d and for n = 3 , d = 2 only. Starting with the generating set of C 3 d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C 3 d is equal to 7 for any d ⩾ 3 . We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8. The proofs are based …
Strongly invertible links and divides
2008
Abstract To a proper generic immersion of a finite number of copies of the unit interval in a 2-disc, called a divide, A’Campo associates a link in S 3 . From the more general notion of ordered Morse signed divides, one obtains a braid presentation of links of divides. In this paper, we prove that every strongly invertible link is isotopic to the link of an ordered Morse signed divide. We give fundamental moves for ordered Morse signed divides and show that strongly invertible links are equivalent if and only if we can pass from one ordered Morse signed divide to the other by a sequence of such moves. Then we associate a polynomial to an ordered Morse signed divide, invariant for these move…
L 2-topological invariants of 3-manifolds
1995
We give results on theL2-Betti numbers and Novikov-Shubin invariants of compact manifolds, especially 3-manifolds. We first study the Betti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequence of chain complexes. Our algebraic results, along with some analytic results on geometric 3-manifolds, are used to compute theL2-Betti numbers of compact 3-manifolds which satisfy a weak form of the geometrization conjecture, and to compute or estimate their Novikov-Shubin invariants.
Sobolev embeddings, extensions and measure density condition
2008
AbstractThere are two main results in the paper. In the first one, Theorem 1, we prove that if the Sobolev embedding theorem holds in Ω, in any of all the possible cases, then Ω satisfies the measure density condition. The second main result, Theorem 5, provides several characterizations of the Wm,p-extension domains for 1<p<∞. As a corollary we prove that the property of being a W1,p-extension domain, 1<p⩽∞, is invariant under bi-Lipschitz mappings, Theorem 8.
Minimal forbidden words and symbolic dynamics
1996
We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system defined by L.