共查询到20条相似文献,搜索用时 78 毫秒
1.
We give a detailed study of dynamical properties of the Zhang model, including evaluation of topological entropy and estimates
for the Lyapunov exponents and the dimension of the attractor. In the thermodynamic limit the entropy goes to zero and the
Lyapunov spectrum collapses. 相似文献
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3.
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement–deconfinement transitions in the corresponding gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed. 相似文献
4.
Howard Weiss 《Journal of statistical physics》1992,69(3-4):879-886
We derive several variational formulas for the topological entropy and SRB entropy of Axiom A flows on compact manifolds and for the Hausdorff dimension of basic sets for Axiom A diffeomorphisms on compact surfaces. 相似文献
5.
A. López-Ortega 《General Relativity and Gravitation》2010,42(12):2939-2945
There are exact solutions to Einstein’s equations with negative cosmological constant that represent black holes whose event horizons are manifolds of negative curvature, the so-called topological black holes. Among these solutions there is one, the massless topological black hole, whose mass is equal to zero. Hod proposes that in the semiclassical limit the asymptotic quasinormal frequencies determine the entropy spectrum of the black holes. Taking into account this proposal, we calculate the entropy spectrum of the massless topological black hole and we compare with the results on the entropy spectra of other topological black holes. 相似文献
6.
Feynman-graph rules are formulated for the strong—interaction components of the topological expansion—defined as those graphs all of whose vertices are zero—entropy connected parts. These rules imply a “topological asymptotic freedom” and admit a corresponding perturbative evaluation where the zeroth order exhibits topological supersymmetry. 相似文献
7.
Albert Fathi 《Communications in Mathematical Physics》1989,126(2):249-262
We show that there exists a simple upper bound on the dimension of a hyperbolic compact set of a dynamical system in terms of topological entropy and a uniform contraction rate on the stable and unstable manifolds. This allows us to give proofs of several apparently unrelated theorems. 相似文献
8.
Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows
Anatole Katok Gerhard Knieper Howard Weiss 《Communications in Mathematical Physics》1991,138(1):19-31
This paper represents part of a program to understand the behavior of topological entropy for Anosov and geodesic flows. In this paper, we have two goals. First we obtain some regularity results forC
1 perturbations. Second, and more importantly, we obtain explicit formulas for the derivative of topological entropy. These formulas allow us to characterize the critical points of topological entropy on the space of negatively curved metrics.Partially supported by NSF grant DMS-8514630Chaim Weizmann Research Fellow and NSF postdoctoral Research Fellow 相似文献
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Miaohua Jiang 《Journal of statistical physics》1999,95(3-4):791-803
We give a detailed proof of the entropy formula for SRB-measures of coupled hyperbolic attractors over integer lattices. We show that the topological pressure for the potential function of the SRB-measure is zero. 相似文献
11.
A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, di, F(lmn)(ijk), delta(ijk). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the "topological entropy" which directly measures the total quantum dimension D= Sum(id2i). 相似文献
12.
Delone sets of finite local complexity in Euclidean space are investigated. We show that such a set has patch counting and
topological entropy zero if it has uniform cluster frequencies and is pure point diffractive. We also note that the patch
counting entropy vanishes whenever the repetitivity function satisfies a certain growth restriction.
相似文献
13.
《Physica D: Nonlinear Phenomena》1986,19(2):206-237
Many biperiodic flows can be modelled by maps of a circle to itself. For such maps the transition from zero to positive topological entropy can be achieved in several ways. We describe all the possible routes for smooth circle maps, and discuss the relevance of our results to the transition to chaos for two-frequency systems. 相似文献
14.
Troubetzkoy S 《Chaos (Woodbury, N.Y.)》1998,8(1):242-244
Polygonal billiards have zero topological entropy. Complexity is a finer measure of their asymptotic behavior. In this article we show an explicit quadratic lower bound for the complexity of the billiard in an arbitrary polygon. (c) 1998 American Institute of Physics. 相似文献
15.
A. Katok 《Communications in Mathematical Physics》1987,111(1):151-160
For any simply connected polygon in the plane, the number of billiard orbits which begin and end at a vertex grows subexponentially with respect to the length or to the number of reflections. This implies that the numbers of isolated periodic orbits and of families of parallel periodic orbits do grow subexponentially. The main technical device is a calculation showing that the topological entropy of the Poincaré map for the billiard flow is equal to zero.Supported in part by NSF Grant #DMS-8414400 相似文献
16.
Kazuhiro Hikami 《Annals of Physics》2008,323(7):1729-1769
We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read-Rezayi state whose effective theory is the SU(2)K Chern-Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems. 相似文献
17.
The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincare? return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model. 相似文献
18.
This paper presents an answer to an open problem in the dynamical systems of three letters: the generalized Milnor–Thurston
conjecture on the existence of infinitely many plateaus of topological entropy in the two-dimensional parameter plane. The
concept of equal topological entropy class is introduced by the dual star product which is a generalization of the Derrida–Gervois–Pomeau
star product to the symbolic dynamics of three letters for the endomorphisms on the interval. The algebraic rules established
by the dual star products for the doubly superstable kneading sequences are equivalent to the normal factorization of the
Milnor–Thurston characteristic polynomials. Moreover, the classification theory of symbolic primitive and compound sequences
based on the topological conjugacy in the meaning of equal entropy is completed in the topological space Σ3 of three letters.
Received: 4 February 1998 / Accepted: 1 March 2000 相似文献
19.
David Kerr 《Communications in Mathematical Physics》2003,232(3):501-534
We introduce notions of dimension and dynamical entropy for unital C
*
-algebras ``metrized' by means of , which are complex-scalar versions of the Lip-norms constitutive of Rieffel's compact quantum metric spaces. Our examples
involve the UHF algebras and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the
canonical coincides with the topological entropy of its commutative analogue.
Received: 13 February 2002 / Accepted: 20 August 2002 Published online: 22 November 2002 相似文献
20.
本文推广了文献[1]的工作,并用逆轨道分析法说明了本文所列公式的证明。据此可以算出整个参数区间中任一点上的拓扑熵值。在讨论“*”乘对拓扑熵值影响的基础上得到了一维映象拓扑熵的整体印象。
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