We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and the...We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.展开更多
Let P and AC be two primary sequences with min{P, AC} RLR<sup>∞</sup>,ρ（P） and p（AC） be the eigenvalues of P and AC, respectively. Let f ∈ C<sup>0</sup>（I, I） be a unimodal expanding m...Let P and AC be two primary sequences with min{P, AC} RLR<sup>∞</sup>,ρ（P） and p（AC） be the eigenvalues of P and AC, respectively. Let f ∈ C<sup>0</sup>（I, I） be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved that f has the kneading sequence K（f） （RC）<sup>*m</sup> * P if λ （ρ（P））<sup>1/2<sup>m</sup></sup>, and K（f）】（RC）<sup>*m</sup> * AC * E for any shift maximal sequence E if λ】（ρ（AC））<sup>1/2<sup>m</sup></sup>. The value of （ρ（P））<sup>1/2<sup>m</sup></sup> or （ρ（AC））<sup>1/2<sup>m</sup></sup> is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.展开更多
We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities a...We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.展开更多
Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...,n_k such that Per(f)is contained in ∪_i^k=1 ∪_j~∞=0 n_i2~j,where Edg(G) is the number of edges of G and End(G)is the number of end points of G.展开更多
The biological </span><span style="font-family:Verdana;font-size:12px;">principal</span><span style="font-family:Verdana;font-size:12px;"> or its detailed mechanism for the ...The biological </span><span style="font-family:Verdana;font-size:12px;">principal</span><span style="font-family:Verdana;font-size:12px;"> or its detailed mechanism for the pandemic coronavirus disease 2019 (COVID-19) has been investigated and analyzed from the topological entropy approach. The findings thus obtained have provided very useful clues and information for developing both powerful and safe vaccines against the pandemic COVID-19.展开更多
基金Supported by NNSF of China(Grant Nos.11371339,11431012,11401362,11471125)NSF of Guangdong province(Grant No.S2013040014084)
文摘We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
基金Project supported by the National Natural Science Foundation of China
文摘Let P and AC be two primary sequences with min{P, AC} RLR<sup>∞</sup>,ρ（P） and p（AC） be the eigenvalues of P and AC, respectively. Let f ∈ C<sup>0</sup>（I, I） be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved that f has the kneading sequence K（f） （RC）<sup>*m</sup> * P if λ （ρ（P））<sup>1/2<sup>m</sup></sup>, and K（f）】（RC）<sup>*m</sup> * AC * E for any shift maximal sequence E if λ】（ρ（AC））<sup>1/2<sup>m</sup></sup>. The value of （ρ（P））<sup>1/2<sup>m</sup></sup> or （ρ（AC））<sup>1/2<sup>m</sup></sup> is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.
基金The NSF (10271057 and 10571086) of ChinaQing-lan Project in Nanjing Universityof Posts and Telecommunications (NY206053)
文摘We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.
基金Project supported by NSF (10171034) of ChinaNSF (970395) of Guangdong province
文摘Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...,n_k such that Per(f)is contained in ∪_i^k=1 ∪_j~∞=0 n_i2~j,where Edg(G) is the number of edges of G and End(G)is the number of end points of G.
文摘The biological </span><span style="font-family:Verdana;font-size:12px;">principal</span><span style="font-family:Verdana;font-size:12px;"> or its detailed mechanism for the pandemic coronavirus disease 2019 (COVID-19) has been investigated and analyzed from the topological entropy approach. The findings thus obtained have provided very useful clues and information for developing both powerful and safe vaccines against the pandemic COVID-19.
