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121.
A new method for computing the topological entropy of a piecewise monotonic transformation on the interval is presented. It uses a transition matrix associated with the transformation. For this matrix we give a spectral theorem. This can be used for an estimation of the accuracy of the algorithm. 相似文献
122.
Mitchell J. Feigenbaum 《Journal of statistical physics》1987,46(5-6):925-932
The grand canonical version of the spectrum of singularities formalism is presented, relying naturally upon certain Markov transition graphs. The structure of a graph is simply determined by the close return times of the dynamical system described. Thus, an intimate connection exists between the shape of the singularity curve and a small but interesting set of dynamical properties. 相似文献
123.
Jeffrey Goldstein 《Nonlinear dynamics, psychology, and life sciences》2001,5(3):197-204
This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice. Finally, there is a discussion of how such strategies for understanding paradox transcend the realm of empirical research and enter territory in the philosophy of mathematics. 相似文献
124.
Martin Rasmussen 《Proceedings of the American Mathematical Society》2008,136(3):1045-1055
Morse decompositions provide inside information about the global asymptotic behavior of dynamical systems on compact metric spaces. Recently, the existence of Morse decompositions for nonautonomous dynamical systems was proved by restricting attention to the past or the future of the system, but in general, such a construction is not realizable for the entire time. In this article, it is shown that all-time Morse decompositions can be defined for linear systems on the projective space. Moreover, the dynamical properties are discussed and an analogue to the Theorem of Selgrade is proved.
125.
We perform the Borel resummation of the currently known terms of the ɛ-expansion up to order ɛ
4
of the dynamical exponent z in the critical-behavior model A. We obtain the large-order asymptotic approximation of the ɛ-expansion
of the dynamical exponent and find a significant discrepancy between the currently calculated orders of the expansion and
the obtained asymptotic values. We discuss the influence of this deviation on the accuracy of the resummation results.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 1, pp. 96–108, April, 2009. 相似文献
126.
N. Pitsianis Ph. Tsalides G. L. Bleris A. Thanailakis H. C. Card 《Journal of statistical physics》1989,56(1-2):99-112
A formal treatment of some of the properties of deterministic, rule 150, elementary one-dimensional cellular automata (CA) with null boundary conditions is presented. The general form of the characteristic polynomial of the CA global rule transition matrix is obtained. Mathematical relationships between the CA register lengths and the order of the corresponding group or semigroup structures are derived. 相似文献
127.
A study of the d.ynamical fluctuation properties at various c.m.energies in e~ e~- collisions is performed using the Monte Carlo method.The results suggest that,after the normalized factorial moments of 3-dimensional phase space are analyzed using an isotropical phase space partition,the NFM describing non- linear dynamical properties show a power-law scaling,i.e.,the dynamical fluctuations in higher dimensional phase space are isotropic.For c.m.energies s~(1/2)≤80 GeV,the scaling exponentsφ_q increase rapidly with the c.m.energy and for c.m.energies s~(1/2)>80 GeV,theφ_q gradually saturate. 相似文献
128.
We study the existence of non-collision periodic solutions for second order singular dynamical systems. The repulsive case and the attractive case are dealt with using a unified topological approach. The proof is based on a well-known fixed point theorem for completely continuous operators, involving a new type of cone. We do not need to consider so-called strong force conditions. Moreover, for the repulsive case, the critical case can be covered. Recent results in the literature, even in the scalar case, are complemented, generalized and improved. 相似文献
129.
In this paper, we first present some sufficient conditions for the existence of a global random attractor for general stochastic lattice dynamical systems. These sufficient conditions provide a convenient approach to obtain an upper bound of Kolmogorov ε-entropy for the global random attractor. Then we apply the abstract result to the stochastic lattice sine-Gordon equation. 相似文献
130.
Haixia Wang Qishao Lu Qingyun Wang 《Communications in Nonlinear Science & Numerical Simulation》2008,13(8):1668-1675
Bursting is an important electrical behavior in neuron’s firing. In this paper, based on the fast/slow dynamical bifurcation analysis and the phase plane analysis, two types of bursting are presented in the modified Morris–Lecar neuronal model, and the associated bifurcation mechanisms of switching between the active phase and the silent phase are analyzed. For two coupled bursters, it is found that the same type of coupled bursters may have different synchronization transition path from that of two different types of coupled bursters. The analysis of bursting types and the transition to synchronization may provide us with better insight into neuronal encoding and information transmission. 相似文献