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  • Family of chaotic maps from game theory
    Dyn. Syst. (IF 0.986) Pub Date : 2020-07-20
    Thiparat Chotibut; Fryderyk Falniowski; Michał Misiurewicz; Georgios Piliouras

    From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal, on which a two-parameter family of bimodal interval maps exhibits periodic orbits and chaos. While the fixed point b corresponding to a Nash equilibrium of such

    更新日期:2020-07-21
  • On the topological entropy of induced transformations for free semigroup action
    Dyn. Syst. (IF 0.986) Pub Date : 2020-07-20
    Yong Ji; Yunping Wang

    The aim of this paper is to reveal the relationship between the topological entropy of a free semigroup action and that of its induced transformations. More precisely, we prove that the topological entropy of a free semigroup action ( X , F ) vanishes if and only if the topological entropy of its induced system ( M ( X ) , F ) is zero; if the topological entropy of ( X , F ) is positive, then that

    更新日期:2020-07-21
  • Relative Equilibria, Stability and Bifurcations in Hamiltonian Galactic-Tidal Models
    Dyn. Syst. (IF 0.986) Pub Date : 2020-07-10
    J. L. Zapata; F. Crespo; S. Ferrer

    We study special solutions of Galactic-Tidal models and the existence, stability and bifurcations of relative equilibria. Precisely, we found four equilibria and rectilinear, as well as circular solutions, previous to any manipulation of the original system. Moreover, by averaging of the Keplerian energy and making use of Reeb's theorem, we find four periodic orbits. The stability of these relative

    更新日期:2020-07-10
  • Asymptotic behavior of stochastic heat equations in materials with memory on thin domains
    Dyn. Syst. (IF 0.986) Pub Date : 2020-07-09
    Ji Shu; Hui Li; Xin Huang; Jian Zhang

    This paper deals with the dynamical behavior of a stochastic integro-differential equation driven by additive noise defined on thin domains. We prove the existence and uniqueness of random attractors for the equation in an ( n + 1 ) -dimensional narrow domain. Due to the fact that the memory term includes the whole past history of the phenomenon, we are not able to prove compactness of the generated

    更新日期:2020-07-09
  • On the regularity and approximation of invariant densities for random continued fractions
    Dyn. Syst. (IF 0.986) Pub Date : 2020-06-30
    Toby Taylor-Crush

    We study perturbations of random dynamical systems whose associated transfer operators admit a uniform spectral gap. We provide a k t h -order approximation for the invariant density of the associated random dynamical system. We apply our result to random continued fractions.

    更新日期:2020-06-30
  • A Central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation
    Dyn. Syst. (IF 0.986) Pub Date : 2020-06-12
    Tanja I. Schindler

    We prove a central limit theorem for the real and imaginary part and the absolute value of the Riemann zeta-function sampled along a vertical line in the critical strip with respect to an ergodic transformation similar to the Boolean transformation. This result complements a result by Steuding who has proven a strong law of large numbers for the same system. As a side result we state a general central

    更新日期:2020-06-12
  • Global dynamics of the Maxwell-Bloch system with invariant algebraic surfaces
    Dyn. Syst. (IF 0.986) Pub Date : 2020-06-01
    F.S. Dias; Claudia Valls

    In this paper by using the Poincaré compactification in R3 we make a global analysis of the Maxwell-Bloch system x˙=y,y˙=cy+dx−xzz˙=bz+xy with (x,y,z)∈R3, b,c and d∈R. We give the complete description of its dynamics on the sphere at infinity. For some values of the the parameters, this system has first integrals and invariant algebraic surfaces. For these sets we provide the global phase portraits

    更新日期:2020-06-01
  • Decomposition of stochastic flow and an averaging principle for slow perturbations
    Dyn. Syst. (IF 0.986) Pub Date : 2020-05-18
    Diego Sebastian Ledesma; Fabiano Borges da Silva

    We use decomposition of stochastic flow to obtain components that represent the slow and fast motion of a given perturbed stochastic differential equation. Then, through a special metric which works well with stochastic calculation tools, Lipschitz condition for vector fields and an averaging principle we obtain an approximation for the slow motion. Finally, we get an estimate for the approximation

    更新日期:2020-05-18
  • Orbit Growth of Dyck and Motzkin Shifts via Artin-Mazur Zeta Function
    Dyn. Syst. (IF 0.986) Pub Date : 2020-05-18
    Azmeer Nordin; Mohd Salmi MdNoorani; Syahida Che Dzul-Kifli

    For a discrete dynamical system, the prime orbit and Mertens' orbit counting functions indicate the growth of the closed orbits in the system in a certain way. In this paper, we prove the asymptotic behaviours of the counting functions for Dyck and Motzkin shifts. The proof relies on the analyticity and non-vanishing property of their Artin-Mazur zeta functions.

    更新日期:2020-05-18
  • Geometry of symplectic partially hyperbolic automorphisms on 4-torus
    Dyn. Syst. (IF 0.986) Pub Date : 2020-05-04
    L.M. Lerman; K.N. Trifonov

    We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism. There are two different cases, transitive and decomposable ones. For both cases the classification is given.

    更新日期:2020-05-04
  • Equicontinuity and Li-Yorke pairs of dendrite maps
    Dyn. Syst. (IF 0.986) Pub Date : 2020-04-22
    Ghassen Askri

    In this paper, relationships between equicontinuity of a dendrite map f on Λ(f), absence of Li-Yorke pairs, collection of minimal sets and regularly recurrent points are investigated.

    更新日期:2020-04-22
  • Minimality of 5-adic polynomial dynamics
    Dyn. Syst. (IF 0.986) Pub Date : 2020-03-30
    Donggyun Kim; Youngwoo Kwon; Kyunghwan Song

    We characterize the dynamical systems consisting of the set of 5-adic integers and polynomial maps which consist of one minimal component.

    更新日期:2020-03-30
  • On inverse shadowing
    Dyn. Syst. (IF 0.986) Pub Date : 2020-03-18
    Chris Good; Joel Mitchell; Joe Thomas

    We give a reformulation of the inverse shadowing property with respect to the class of all pseudo-orbits. This reformulation bears witness to the fact that the property is far stronger than might initially seem. We give some implications of this reformulation, in particular showing that systems with inverse shadowing are not sensitive. Finally we show that, on compact spaces, inverse shadowing is equivalent

    更新日期:2020-03-18
  • Optimal quantization via dynamics
    Dyn. Syst. (IF 0.986) Pub Date : 2020-03-14
    Joseph Rosenblatt; Mrinal Kanti Roychowdhury

    Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using stationary processes arising in dynamical systems, followed by a discussion of the special cases of stationary processes: random processes and Diophantine processes

    更新日期:2020-03-14
  • Dimensions in infinite iterated function systems consisting of bi-Lipschitz mappings
    Dyn. Syst. (IF 0.986) Pub Date : 2020-03-10
    Chih-Yung Chu; Sze-Man Ngai

    We study infinite iterated function systems (IIFSs) consisting of bi-Lipschitz mappings instead of conformal contractions, focussing on IFSs that do not satisfy the open set condition. By assuming the logarithmic distortion property and some cardinality growth condition, we obtain a formula for the Hausdorff, box, and packing dimensions of the limit set in terms of certain topological pressure. By

    更新日期:2020-03-10
  • Weak Gibbs measures and equilibrium states
    Dyn. Syst. (IF 0.986) Pub Date : 2020-02-18
    Maria Carvalho; Sebastián A. Pérez

    We present a simple proof of the fairly general fact that an invariant right-weak Gibbs probability measure is an equilibrium state, using a generalization of the formula of Brin and Katok for the local metric entropy. This new formula also allows us to clarify the role of the topological pressure on the standard definition of the Gibbs property.

    更新日期:2020-02-18
  • Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields
    Dyn. Syst. (IF 0.986) Pub Date : 2020-02-10
    João L. Cardoso; Jaume Llibre; Douglas D. Novaes; Durval J. Tonon

    In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has centre, a real one for y<0 and a virtual one for y>0, and such that

    更新日期:2020-02-10
  • A groupoid approach to C*-algebras associated with λ-graph systems and continuous orbit equivalence of subshifts
    Dyn. Syst. (IF 0.986) Pub Date : 2020-02-05
    Kengo Matsumoto

    A λ-graph system L is a labelled Bratteli diagram with shift operation. It is a generalized notion of finite labelled graph and presents a subshift. We will study continuous orbit equivalence of one-sided subshifts and topological conjugacy of two-sided subshifts from the view points of groupoids and C∗-algebras constructed from λ-graph systems.

    更新日期:2020-02-05
  • Limsup is needed in the definitions of topological entropy via spanning or separation numbers
    Dyn. Syst. (IF 0.986) Pub Date : 2020-02-04
    Winfried Just; Ying Xin

    ABSTRACT The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution ϵ within T time units. It can then be formally defined as a limit of a limit superior that involves either covering numbers, or separation numbers, or spanning numbers. If covering numbers are used, the limit superior reduces to a limit. While it has

    更新日期:2020-02-04
  • Weighted upper metric mean dimension for amenable group actions
    Dyn. Syst. (IF 0.986) Pub Date : 2020-01-07
    Dingxuan Tang; Haiyan Wu; Zhiming Li

    In this paper, we formulate the notions of weighted upper metric mean dimensions and weighted upper measure-theoretic mean dimensions for amenable group actions. In particular, a variational principle for amenable group actions is presented. We also define weighted upper metric mean dimensions with respect to pseudo-orbits and establish their relation to weighted upper metric mean dimensions.

    更新日期:2020-01-07
  • The measures of shadowable pseudo-orbits
    Dyn. Syst. (IF 0.986) Pub Date : 2019-12-28
    Kazuhiro Sakai; Naoya Sumi

    Let f be a continuous map of a compact metric space. In Moriyasu et al. [Diffeomorphisms with shadowable measures, Axioms 7(4) (2018), p. 93. Available at https://doi.org/10.3390/axioms7040093], the notion of shadowable measures for f is introduced, and the property of dynamical systems admitting shadowable measures is studied. In this paper, we introduce a probability measure on the space of pseudo-orbits

    更新日期:2019-12-28
  • On the dynamics of the Euler equations on so(4)
    Dyn. Syst. (IF 0.986) Pub Date : 2019-12-22
    Claudio A. Buzzi; Jaume Llibre; Rubens Pazim

    This paper deals with the Euler equations on the Lie Algebra so(4). These equations are given by a polynomial differential system in R 6 . We prove that this differential system has four 3-dimensional invariant manifolds and we give a complete description of its dynamics on these invariant manifolds. In particular, each of these invariant manifolds are fulfilled by periodic orbits except in a zero

    更新日期:2019-12-22
  • Equivalent notions of hyperbolicity
    Dyn. Syst. (IF 0.986) Pub Date : 2019-12-18
    Luis Barreira; Claudia Valls

    For a linear nonautonomous dynamics, we give a characterization of its hyperbolicity in terms of a certain cocycle, both for discrete and continuous time. The base of the cocycle is obtained taking the closure of the translations of the dynamics with respect to the topology of uniform convergence on compact sets, which in the case of discrete time corresponds to pointwise convergence.

    更新日期:2019-12-18
  • Suspensions of homeomorphisms with the two-sided limit shadowing property
    Dyn. Syst. (IF 0.986) Pub Date : 2019-11-25
    Jesús Aponte; Bernardo Carvalho; Welington Cordeiro

    In this paper, we discuss the two-sided limit shadowing property for continuous flows defined in compact metric spaces. We analyse some of the results known for the case of homeomorphisms in the case of continuous flows and observe that some differences appear in this scenario. We prove that the suspension flow of a homeomorphism satisfying the two-sided limit shadowing property also satisfies it.

    更新日期:2019-11-25
  • Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type
    Dyn. Syst. (IF 0.986) Pub Date : 2019-10-06
    Marc Kesseböhmer; Tanja I. Schindler

    We prove strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type. This gives another application of a previous trimming result only proven for interval maps. To prove these statements we introduce the space of quasi-Hölder continuous functions for subshifts of finite type. Additionally, we prove a trimmed strong law for St. Petersburg type distribution

    更新日期:2019-10-06
  • Leafwise shadowing property for partially hyperbolic diffeomorphisms
    Dyn. Syst. (IF 0.986) Pub Date : 2019-09-26
    A. Castro; F. Rodrigues; P. Varandas

    In this note, we characterize hyperbolicity of invariant laminations for partially hyperbolic diffeomorphisms in terms of a leafwise shadowing property. We prove that a C 1 -diffeomorphism with partially hyperbolic non-wandering set is Axiom A if and only if the leafwise shadowing property holds along the central lamination for all C 1 -close diffeomorphisms. Similar results hold for open classes of

    更新日期:2019-09-26
  • On the computation of extended rescaled Poincaré maps for singular vector fields
    Dyn. Syst. (IF 0.986) Pub Date : 2019-09-23
    Qianying Xiao; Yiwei Zhang

    In this paper, we aim to compute extended rescaled Poincaré maps for singular vector fields. For explicit 2-dimensional linear vector fields, we are able to compute the extended rescaled Poincaré maps upto second order derivatives. For singular vector fields, we show that the extended rescaled Poincaré maps over the non-degenerate singularity are equal to the extended rescaled Poincaré maps of the

    更新日期:2019-09-23
  • Almost-periodic bifurcations for one-dimensional degenerate vector fields
    Dyn. Syst. (IF 0.986) Pub Date : 2019-09-23
    Wen Si; Xiaodan Xu; Jianguo Si

    Quasi-periodic high order degenerate bifurcation theories have been well established, but works which are related to almost-periodic bifurcations seem to be very few. In this paper, we consider the almost-periodic time-dependent perturbations of one-dimensional degenerate vector field x ˙ = x l . With the KAM theory and singularity theory, we show that the universal unfolding of the vector field can

    更新日期:2019-09-23
  • Gibbs states and Gibbsian specifications on the space ℝℕ
    Dyn. Syst. (IF 0.986) Pub Date : 2019-09-18
    Artur O. Lopes; Victor Vargas

    We are interested in the study of Gibbs and equilibrium probabilities on the space state R N . We consider the unilateral full-shift σ defined on the non-compact set R N , that is σ ( x 1 , x 2 , . . , x n , . . ) = ( x 2 , x 3 , . . , x n , . . ) , and a Hölder continuous potential A : R N → R . From a suitable class of a priori probability measures ν we define the Ruelle operator associated to A

    更新日期:2019-09-18
  • On the equivariance properties of self-adjoint matrices
    Dyn. Syst. (IF 0.986) Pub Date : 2019-09-18
    Michael Dellnitz; Bennet Gebken; Raphael Gerlach; Stefan Klus

    We investigate self-adjoint matrices A ∈ R n , n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ 2 ( A ) ⊂ O ( n ) which is isomorphic to ⊗ k = 1 n Z 2 . If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an

    更新日期:2019-09-18
  • Volume of the hyperbolic cantor sets
    Dyn. Syst. (IF 0.986) Pub Date : 2019-09-16
    Habibulla Akhadkulov; Yunping Jiang

    In this paper, we study hyperbolic Cantor sets on the line. We prove that the Lebesgue measure of a hyperbolic Cantor set generated by a degree two expanding map satisfying a certain Zygmund condition is zero. Moreover, we show that for any ρ ∈ ( 0 , 1 ) there exists a C 1 -smooth degree two expanding map f such that the Lebesgue measure of the hyperbolic Cantor set generated by f is ρ.

    更新日期:2019-09-16
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