Quantifying chaos: a tale of two maps

In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov exponents should demonstrate evidence of convergence; but literature abounds in which this evidence lacks. This paper presents two maps through which it highlights the importance of providing evidence of convergence of Lyapunov exponent estimates. The results suggest cautious conclusions when confronted with real data. Moreover, the maps are interesting in their own right.

A tale of two Montreal communities: parental perspectives on their children's multi-lingual and multi-literate development

This comparative inquiry examines the multi-/bilingual nature and cultural diversity of two distinctly different linguistic and ethnic communities in Montreal – English speakers and Chinese speakers – with a focus on the multi/bilingual and multi/biliterate development of children from these two communities who attend French-language schools, by choice in one case and by law in the other. In both of these communities, children traditionally achieve academic success. The authors approach this investigation from the perspective of the parents’ aspirations and expectations for, and their support of and involvement in, their children’s education. These two communities share key similarities and differences that, when considered together, help to clarify a number of issues involving multi/biliteracy development, socio-economic and linguistic capital, minority/majority language status, mother-tongue support, home–school continuities, and linguistic identity.