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Article
Multiply minimal points for the product of iterates
The multiple Birkhoff recurrence theorem states that for any d ∈ ℕ, every system (X, T) has a multiply recurrent point x, i.e., (x, x, …, x) is recurrent under τd ≕ T × T2 × ⋯ × Td. It is natural to ask if there ...
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Article
Local stable and unstable sets for positive entropy C1 dynamical systems
For any C1 diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy, a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in ...
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Article
Regionally proximal relation of order d along arithmetic progressions and nilsystems
The regionally proximal relation of order d along arithmetic progressions, namely AP[d] for d ∈ ℕ, is introduced and investigated. It turns out that if (X, T) is a topological dynamical system with AP[d] = Δ, the...
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Article
Finite Intersection Property and Dynamical Compactness
Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800–6827, 2016). In this paper we continue to...
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Article
Steady States of Fokker–Planck Equations: III. Degenerate Diffusion
This is the third paper in a series concerning the study of steady states of a Fokker–Planck equation in a general domain in $${\mathb...
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Article
Riemannian Optimization for Registration of Curves in Elastic Shape Analysis
In elastic shape analysis, a representation of a shape is invariant to translation, scaling, rotation, and reparameterization, and important problems such as computing the distance and geodesic between two cur...
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Article
Invariant scrambled sets, uniform rigidity and weak mixing
We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant δ-scrambled set fo...
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Article
Steady States of Fokker–Planck Equations: II. Non-existence
This is the second paper in a series concerning the study of steady states, including stationary solutions and measures, of a Fokker–Planck equation in a general domain in
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Article
Steady States of Fokker–Planck Equations: I. Existence
This is the first paper in a series concerning the study of steady states of a Fokker–Planck equation in a general domain in $$\mathbb...
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Article
Entropy of Dynamical Systems with Repetition Property
The repetition property of a dynamical system, a notion introduced in Boshernitzan and Damanik (Commun Math Phys 283:647–662, 2008), plays an importance role in analyzing spectral properties of ergodic Schrödinge...
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Article
Measure-theoretical sensitivity and equicontinuity
For an invariant measure µ in a topological dynamics, notions of µ-sensitivity, µ-complexity and µ-equicontinuity are introduced and investigated. It turns out that µ-sensitivity defined here is equivalent to ...
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Article
A local variational principle of pressure and its applications to equilibrium states
We prove a local variational principle of pressure for any given open cover. More precisely, for a given dynamical system (X, T), an open cover ...
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Article
Relative entropy tuples, relative u.p.e. and c.p.e. extensions
Relative entropy tuples both in topological and measure-theoretical settings, relative uniformly positive entropy (rel.-u.p.e.) and relative completely positive entropy (rel.-c.p.e.) are studied. It is shown t...
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Article
A local variational relation and applications
In [BGH] the authors show that for a given topological dynamical system (X,T) and an open coveru there is an invariant measure μ such that infh μ(T,ℙ)≥h top(T,U) where infimum is taken over all partitions finer t...
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Article
Null Flows and Null Functions on \(\mathbb{R}\)
In this paper, we introduce the notion of null flows via sequence entropy. We study the structure of minimal null flows and show that such a flow is almost automorphic and uniquely ergodic. Moreover, minimal n...
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Article
Non-wandering sets of the powers of maps of a tree
Let T be a tree and let Ω ( f ) be the set of non-wandering points of a continuous map f: T→ T. We prove that for a continuous map f: T→ T of a tree T: ( i) if x∈ Ω( f) has an infinite orbit, then x∈ Ω( fn) for e...