Fixed points of log-linear discrete dynamics
نویسندگان
چکیده
منابع مشابه
Fixed Points for Discrete Logarithms
Abstract: We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root r and an integer t in the interval [1, p− 1] with logr t = t. Here, logr is the discrete logarithm function to the base r for the cyclic group (Z/pZ)×. Tools include a numerically explicit version of the Pólya–Vinogradov inequality for the sum of values of a Dirichlet character on an interval, s...
متن کاملFixed points of competitive threshold-linear networks
Threshold-linear networks (TLNs) are models of neural networks that consist of simple, perceptron-like neurons and exhibit nonlinear dynamics that are determined by the network’s connectivity. The set of fixed points of a TLN, including both stable and unstable equilibria, plays a critical role in shaping its emergent dynamics. In this work, we provide two novel characterizations for the set of...
متن کاملStructure of stochastic dynamics near fixed points.
We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where the force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always be defined near it. Such a stationary distribution does not need to satisfy the usual detailed balance condition but might have instead a divergence-fre...
متن کاملRational Fixed Points for Linear Group Actions
Pietro Corvaja §1 Introduction. A general principle in the theory of diophantine equations asserts that if an equation admits " many " rational solutions, there should be a geometric reason explaining such abundance. We consider here a (multiplicative) semigroup of N ×N matrices with rational entries: we suppose that all of them admit rational eigenvalues and deduce the natural geometrical cons...
متن کاملHomotopy fixed points for profinite groups emulate homotopy fixed points for discrete groups
If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point spectrum Z is Map∗(EK+, Z) K , the fixed points of a familiar expression. Similarly, if G is a profinite group and X is a discrete G-spectrum, then X is often given by (HG,X), where HG,X is a certain explicit construction given by a homotopy limit in the category of discrete G-spectra. Thus, in each of two common equi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 1997
ISSN: 1026-0226,1607-887X
DOI: 10.1155/s1026022697000174