It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a constant slope and the same entropy, and if it is additionally transitive then this semiconjugacy is actually a conjugacy. We generalize this result to piecewise continuous piecewise monotone interval maps, and as a consequence, get it also for piecewise monotone g...

a 1993 result of j. llibre, and m. misiurewicz, (theorem a [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. also a 1980 result of l.s. block, j. guckenheimer, m. misiurewicz and l.s. young (lemma 1.5 [3]) states that if g is an a-graph of f then h(g) ? h( f ). in this pap...

Linear classifiers are much faster to learn and test than non-linear ones. On the other hand, non-linear kernels offer improved performance, albeit at the increased cost of training kernel classifiers. To use non-linear mappings with efficient linear learning algorithms, explicit embeddings that approximate popular kernels have recently been proposed. However, the embedding process is often cos...

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

Let X ⊂ CP be an irreducible projective variety. Assume that F : X → X is a rational continuous map. Denote by h(F ) the entropy of F . In [Fri] we showed that h(F ) = logρ(F ) if X is smooth. Here ρ(F ) is the spectral radius of the induced linear map on the homology groups of X over the rationals. In the first part of this paper (§1) we show that this result is valid for any irreducible norma...

Abstract We observe that every map between finite-dimensional normed spaces of the same dimension respects fixed semi-inner products must be automatically a linear isometry. Moreover, we construct uniformly smooth renorming Hilbert space $$\ell _2$$ ℓ 2 and continuous i...

So, suppose that i ◦ f : Z → X is continuous. Since for every α, the projection πα : X → Xα is continuous, πα ◦ (i ◦ f) : Z → Xα is continuous. The map πα ◦ (i ◦ f) = iα ◦ (ρα ◦ f). By the universal property of the subspace topology on Yα, the map iα ◦ (ρα ◦ f) being continuous implies ρα ◦ f : Z → Yα is continuous. So, we have a collection of continuous maps: ρα ◦ f : Z → Yα so by the universa...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

Using methods from Convex Analysis, for each generalized pressure function we define an upper semi-continuous affine entropy-like map, establish abstract variational principle both countably and finitely additive probability measures prove that equilibrium states always exist. We show this conceptual approach imparts a new insight on dynamical systems without measure with maximal entropy, may b...