Remark on a conjecture of Kaplan and Yorke

Controlling system dimension: a class of real systems that obey the Kaplan-Yorke conjecture.

The Kaplan-Yorke conjecture suggests a simple relationship between the fractal dimension of a system and its Lyapunov spectrum. This relationship has important consequences in the broad field of nonlinear dynamics where dimension and Lyapunov exponents are frequently used descriptors of system dynamics. We develop an experimental system with controllable dimension by making use of the Kaplan-Yo...

Note on the Kaplan Yorke Dimension and Linear Transport Coefficients

A number of new relations between the Kaplan Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the linear transport...

Note on the Kaplan { Yorke dimension and lineartransport

A Remark on Martin's Conjecture

We prove that thc strong Martin conjecture is Ihlse. The counterexample is the first-ordcr thcory of inlinitc atomic Boolea11 algcbras. We show that for this class ol'Roolean algchras. the classilication of their (OJ + 01)-clcmcntary theorics can hc rcduccd t:, thc classification of thc elementary thcories of theilquotient algebras ~llodulo thc Frcchi-t ideals. Martin's conjecture is a strength...

A Remark on a Conjecture of Nakajima

Nakajima conjectured in [N] that the transition matrix between certain PBW-basis constructed in [LXZ] and the affine canonical basis is upper triangular with the diagonal entries equal to one and the upper diagonal entries in vZ[v]. In this paper, we show that the transition matrix between the PBW-basis in [LXZ] and the canonical basis is upper triangular with the diagonal entries equal to one ...