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Search: All articles in the CJM digital archive with keyword exponential

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1. CJM Online first

Ducrot, Arnaud; Magal, Pierre; Seydi, Ousmane
A Finite-time Condition for Exponential Trichotomy in Infinite Dynamical Systems
In this article we study exponential trichotomy for infinite dimensional discrete time dynamical systems. The goal of this article is to prove that finite time exponential trichotomy conditions allow to derive exponential trichotomy for any times. We present an application to the case of pseudo orbits in some neighborhood of a normally hyperbolic set.

Keywords:exponential trichotomy, exponential dichotomy, discrete time dynamical systems, difference equations
Categories:34D09, 34A10

2. CJM 2012 (vol 65 pp. 82)

Félix, Yves; Halperin, Steve; Thomas, Jean-Claude
The Ranks of the Homotopy Groups of a Finite Dimensional Complex
Let $X$ be an $n$-dimensional, finite, simply connected CW complex and set $\alpha_X =\limsup_i \frac{\log\mbox{ rank}\, \pi_i(X)}{i}$. When $0\lt \alpha_X\lt \infty$, we give upper and lower bound for $ \sum_{i=k+2}^{k+n} \textrm{rank}\, \pi_i(X) $ for $k$ sufficiently large. We show also for any $r$ that $\alpha_X$ can be estimated from the integers rk$\,\pi_i(X)$, $i\leq nr$ with an error bound depending explicitly on $r$.

Keywords:homotopy groups, graded Lie algebra, exponential growth, LS category
Categories:55P35, 55P62, , , , 17B70

3. CJM 2010 (vol 63 pp. 38)

Brüdern, Jörg; Wooley, Trevor D.
Asymptotic Formulae for Pairs of Diagonal Cubic Equations
We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.

Keywords:exponential sums, Diophantine equations
Categories:11D72, 11P55

4. CJM 2009 (vol 61 pp. 336)

Garaev, M. Z.
The Large Sieve Inequality for the Exponential Sequence $\lambda^{[O(n^{15/14+o(1)})]}$ Modulo Primes
Let $\lambda$ be a fixed integer exceeding $1$ and $s_n$ any strictly increasing sequence of positive integers satisfying $s_n\le n^{15/14+o(1)}.$ In this paper we give a version of the large sieve inequality for the sequence $\lambda^{s_n}.$ In particular, we obtain nontrivial estimates of the associated trigonometric sums ``on average" and establish equidistribution properties of the numbers $\lambda^{s_n} , n\le p(\log p)^{2+\varepsilon}$, modulo $p$ for most primes $p.$

Keywords:Large sieve, exponential sums
Categories:11L07, 11N36

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