Related papers: Shadowable Points for flows

We define shadowable points for homeomorphism on metric spaces. In the compact case we will prove the following results: The set of shadowable points is invariant, possibly nonempty or noncompact. A homeomorphism has the pseudo-orbit…

In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…

We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a…

In this paper, we will show that any geometric Lorenz flow in a definite class satisfies the parameter-shifted shadowing property.

In this work we study the existence of singular flows satisfying shadowing-like properties. More precisely, we prove that if C1 -vector field on a closed manifold induces a chain-recurrent flow containing an attached hyperbolic singularity…

We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering set consisting of the finite number of critical elements (i.e., singularities or closed orbits).…

For continuous self-maps of compact metric spaces, we explore the relationship among the shadowable points, sensitive points, and entropy points. Specifically, we show that (1) if the set of shadowable points is dense in the phase space,…

In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and…

We prove that every singular hyperbolic chain transitive set with a singularity does not admit the shadowing property. Using this result we show that if a star flow has the shadowing property on its chain recurrent set then it satisfies…

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the…

In this paper we show that the chain recurrent set of a flow of automorphisms on a connected Lie group coincides with the central subgroup of the flow, if the group is decomposable. Moreover, in the decomposable case, the flow satisfies the…

In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the…

We study shadowing property for random infinite pseudotrajectories of a continuous map $f$ of a compact metric space. For the cases of transitive maps and transitive attractors we prove a dichotomy: either $f$ satisfies shadowing property…

This paper examines the relationship between shadowing phenomena and the continuity properties of $\omega$-limit sets in dynamical systems. We give a necessary and sufficient condition for a shadowable point to be an upper (resp. a lower)…

In this paper we discuss the two-sided limit shadowing property for continuous flows defined in compact metric spaces. We analyze some of the results known for the case of homeomorphisms in the case of continuous flows and observe that some…

We study shadowing-type properties for set-valued dynamical systems. In particular, we investigate the periodic shadowing property and its relationship with expansivity and chain transitivity. We establish that for positively expansive…

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a…

We show that Lorenz flows have neither limit shadowing property nor average shadowing property nor the asymptotic average shadowing property where the reparametrizations related to these concepts relies on the set of increasing…

Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let $X$…

We study various types of shadowing properties and their implication for C1 generic vector fields. We show that, generically, any of the following three hypotheses implies that an isolated set is topologically transitive and hyperbolic: (i)…