Existence and Distributional Chaos of Points that are Recurrent but Not Banach Recurrent
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-022-10158-x
Abstract: It is well-known that recurrence is typical from the probabilistic perspective in the study of dynamical systems by Poincare recurrence theorem. According to the recurrent frequency (i.e., the probability of finding the orbit of an… read more here.
Keywords: periodic points; recurrent; recurrent points; recurrence ... See more keywords
Cycles in asymptotically stable and chaotic fractional maps
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DOI: 10.1007/s11071-021-06379-2
Abstract: The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the instrument to describe the behavior of systems with the… read more here.
Keywords: periodic points; stable chaotic; asymptotically periodic; asymptotically stable ... See more keywords
Periodic Points of Regular Curve Homeomorphisms
Sign Up to like & getrecommendations! Published in 2021 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-021-00471-z
Abstract: We prove that, if $$f:X\rightarrow X$$ is a regular curve homeomorphism then the set of periodic points is either empty or dense in the set of non-wandering points. Moreover, we prove that each infinite minimal… read more here.
Keywords: periodic points; curve homeomorphisms; regular curve; points regular ... See more keywords
Central periodic points of linear systems
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DOI: 10.1016/j.jde.2020.10.001
Abstract: Abstract In this paper, we introduce the concept of central periodic points of a linear system as points which lies on orbits starting and ending at the central subgroup of the system. We show that… read more here.
Keywords: periodic points; points linear; system; central periodic ... See more keywords
A note on periodic points of dendrite maps and their induced maps
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2016.11.012
Abstract: Abstract Let X be a compact metric space and 2 X be the hyperspace of all nonempty closed subsets of X endowed with the Hausdorff metric. It is well known that for each continuous map… read more here.
Keywords: periodic points; dendrite maps; note periodic; induced maps ... See more keywords
Counting periodic points on quotient varieties over Fq
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DOI: 10.1016/j.jnt.2018.03.023
Abstract: Abstract Let V be a quasiprojective variety defined over F q , and let ϕ : V → V be an endomorphism of V that is also defined over F q . Let G be… read more here.
Keywords: periodic point; periodic points; counting periodic; quotient varieties ... See more keywords
Density of Periodic Points for Lattès maps over Finite Field
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DOI: 10.1016/j.jnt.2021.10.009
Abstract: Let Ld be the Lattès map associated to the multiplication-by-d endomorphism of an elliptic curve E defined over a finite field Fq. We determine the density δ(Ld, q) of periodic points for Ld in P(Fq).… read more here.
Keywords: periodic points; points latt; density periodic; finite field ... See more keywords
Supporting manifolds for high-dimensional Morse-Smale diffeomorphisms with few saddles
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DOI: 10.1016/j.topol.2020.107315
Abstract: We describe the topological structure of closed manifolds of dimension no less than four which admit Morse-Smale diffeomorphisms such that its non-wandering set contains any number of sink periodic points, and any number of source… read more here.
Keywords: supporting manifolds; smale diffeomorphisms; manifolds high; morse smale ... See more keywords
On regular curve homeomorphisms without periodic points
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DOI: 10.1080/10236198.2021.1912030
Abstract: The purpose of this paper is to study the dynamics of regular curve homeomorphisms without periodic points. We prove mainly that they are extensions of irrational rotations of the circle via a mono... read more here.
Keywords: periodic points; curve homeomorphisms; without periodic; regular curve ... See more keywords
Fast growth of the number of periodic points arising from heterodimensional connections
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DOI: 10.1112/s0010437x21007405
Abstract: We consider $C^{r}$-diffeomorphisms ($1 \leq r \leq +\infty$) of a compact smooth manifold having two pairs of hyperbolic periodic points of different indices which admit transverse heteroclinic points and are connected through a blender. We… read more here.
Keywords: periodic points; fast growth; growth number; number periodic ... See more keywords