Add to ORKGStatement and proof of Theorem 1 part (2) modifiedWe show that for the generic continuous maps of the interval and circle which preserve the Lebesgue measure it holds for each k ≥ 1 that the set of periodic points of period k is a Cantor set of Hausdorff dimension zero and of upper box dimension one. Furthermore, building on this result, we show that there is a dense collection of transitive Lebesgue measure preserving interval map whose periodic points have full Lebesgue measure and whose periodic points of period k have positive measure for each k ≥ 1. Finally, we show that the generic continuous maps of the interval which preserve the Lebesgue measure satisfy the shadowing and periodic shadowing property
AbstractThe simplicial equivalent of the Chow, Mallet-Paret and Yorke theorem is proved and applied ...
We prove that shadowing (the pseudo-orbit tracing property), periodic shadowing (tracing periodic ps...
Letg aC 2 generic bimodal map of the circle. We prove that the closure of the union of the order pre...
Abstract. In this paper, we show that all periods of periodic points forced by a pattern for interva...
AbstractWe prove that generic Z2-actions (f,g) on the interval [0,1] have the property that both f a...
Let us denote $\lambda$ the Lebesgue measure on $[0,1]$, put$$ C(\lambda)=\{f\in C([0,1]);\ \forall~...
In this short note, we find that a continuous piecewise monotone interval map f is chaotic in the se...
In this paper, we prove a generalized shadowing lemma. Let f is an element of Diff(M) Assume that A ...
Since its inception in the 1970s at the hands of Feigenbaum and, independently, Coullet and Tresser ...
AbstractSuppose f is a map from an interval [a,b] into itself with a periodic orbit consisting of th...
International audienceWe prove that the chain-transitive sets of C1-generic diffeomorphisms are appr...
AbstractWe obtain two sufficient conditions for an interval self-map to have a chaotic set with posi...
We prove that for C-1 generic diffeomorphisms, every isolated compact invariant set Lambda which sat...
In the paper we use a special geometric structure of selected one-dimensional continua to prove that...
Many examples exist of one-dimensional systems that are topologically conjugate to the shift operato...
AbstractThe simplicial equivalent of the Chow, Mallet-Paret and Yorke theorem is proved and applied ...
We prove that shadowing (the pseudo-orbit tracing property), periodic shadowing (tracing periodic ps...
Letg aC 2 generic bimodal map of the circle. We prove that the closure of the union of the order pre...
Abstract. In this paper, we show that all periods of periodic points forced by a pattern for interva...
AbstractWe prove that generic Z2-actions (f,g) on the interval [0,1] have the property that both f a...
Let us denote $\lambda$ the Lebesgue measure on $[0,1]$, put$$ C(\lambda)=\{f\in C([0,1]);\ \forall~...
In this short note, we find that a continuous piecewise monotone interval map f is chaotic in the se...
In this paper, we prove a generalized shadowing lemma. Let f is an element of Diff(M) Assume that A ...
Since its inception in the 1970s at the hands of Feigenbaum and, independently, Coullet and Tresser ...
AbstractSuppose f is a map from an interval [a,b] into itself with a periodic orbit consisting of th...
International audienceWe prove that the chain-transitive sets of C1-generic diffeomorphisms are appr...
AbstractWe obtain two sufficient conditions for an interval self-map to have a chaotic set with posi...
We prove that for C-1 generic diffeomorphisms, every isolated compact invariant set Lambda which sat...
In the paper we use a special geometric structure of selected one-dimensional continua to prove that...
Many examples exist of one-dimensional systems that are topologically conjugate to the shift operato...
AbstractThe simplicial equivalent of the Chow, Mallet-Paret and Yorke theorem is proved and applied ...
We prove that shadowing (the pseudo-orbit tracing property), periodic shadowing (tracing periodic ps...
Letg aC 2 generic bimodal map of the circle. We prove that the closure of the union of the order pre...