Functions of genus zero for which the fast escaping set has Hausdorff dimension two

We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two

Simply connected fast escaping Fatou components

We give an example of a transcendental entire function with a simply connected fast escaping Fatou component, but with no multiply connected Fatou components. We also give a new criterion for points to be in the fast escaping set

Julia and escaping set spiders' webs of positive area

We study the dynamics of a collection of families of transcendental entire functions which generalises the well-known exponential and cosine families. We show that for functions in many of these families the Julia set, the escaping set and the fast escaping set are all spiders' webs of positive area. This result is unusual in that most of these functions lie outside the Eremenko-Lyubich class B. This is also the first result on the area of a spider's web

Entire functions for which the escaping set is a spider's web

We construct several new classes of transcendental entire functions, f , such that both the escaping set, I(f), and the fast escaping set, A(f), have a structure known as a spider’s web. We show that some of these classes have a degree of stability under changes in the function. We show that new examples of functions for which I(f) and A(f) are spiders’ webs can be constructed by composition, by differentiation, and by integration of existing examples. We use a property of spiders’ webs to give new results concerning functions with no unbounded Fatou components

Functions of genus zero for which the fast escaping set has Hausdorff dimension two

We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two

Maximally and non-maximally fast escaping points of transcendental entire functions

We partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets are shown to have strong dynamical properties. We show that the ntersection of the Julia set with the non-maximally fast escaping set is never empty. The proof uses a new covering result for annuli, which is of wider interest. It was shown by Rippon and Stallard that the fast escaping set has no bounded components. In contrast, by studying a function considered by Hardy, we give an example of a transcendental entire function for which the maximally and non-maximally fast escaping sets each have uncountably many singleton components

Healthy ageing and home: The perspectives of very old people in five European countries

This paper reports on in-depth research, using a grounded theory approach, to examine the ways in which very old people perceive healthy ageing in the context of living alone at home within urban settings in five European countries. This qualitative study was part of a cross-national project entitled ENABLE-AGE which examined the relationship between home and healthy ageing. Interviews explored the notion of healthy ageing, the meaning and importance of home, conceptualisations of independence and autonomy and links between healthy ageing and home. Data analysis identified five ways in which older people constructed healthy ageing: home and keeping active; managing lifestyles, health and illness; balancing social life; and balancing material and financial circumstances. Older people reflected on their everyday lives at home in terms of being engaged in purposeful, meaningful action and evaluated healthy ageing in relation to the symbolic and practical affordances of the home, contextualised within constructions of their national context. The research suggests that older people perceive healthy ageing as an active achievement, created through individual, personal effort and supported through social ties despite the health, financial and social decline associated with growing older. The physicality and spatiality of home provided the context for establishing and evaluating the notion of healthy ageing, whilst the experienced relationship between home, life history and identity created a meaningful space within which healthy ageing was negotiated

Beyond ‘witnessing’: children’s experiences of coercive control in domestic violence and abuse

Children’s experiences and voices are underrepresented in academic literature and professional practice around domestic violence and abuse. The project ‘Understanding Agency and Resistance Strategies’ addresses this absence, through direct engagement with children. We present an analysis from interviews with 21 children in the United Kingdom (12 girls and 9 boys, aged 8-18 years), about their experiences of domestic violence and abuse, and their responses to this violence. These interviews were analysed using interpretive interactionism. Three themes from this analysis are presented: a) ‘Children’s experiences of abusive control’, which explores children’s awareness of controlling behaviour by the adult perpetrator, their experience of that control, and its impact on them; b) ‘Constraint’, which explores how children experience the constraint associated with coercive control in situations of domestic violence, and c) ‘Children as agents’ which explores children’s strategies for managing controlling behaviour in their home and in family relationships. The paper argues that, in situations where violence and abuse occurs between adult intimate partners, children are significantly impacted, and can be reasonably described as victims of abusive control. Recognising children as direct victims of domestic violence and abuse would produce significant changes in the way professionals respond to them, by 1) recognising children’s experience of the impact of domestic violence and abuse; 2) recognising children’s agency, undermining the perception of them as passive ‘witnesses’ or ‘collateral damage’ in adult abusive encounters; and 3) strengthening professional responses to them as direct victims, not as passive witnesses to violence

Place (in)securities: older adults’ perceptions across urban environments in the United Kingdom ((In)seguridades de lugar. Percepciones de las personas mayores en distintos entornos urbanos del Reino Unido)

This paper explores empirical accounts of perceived insecurities and accompanying issues that make urban place problematic and can impact older adults’ well-being and overall quality of life. Findings reported derive from the project ‘Place-Making with Older People: Towards Age-Friendly Communities’ which investigates both barriers and facilitators to developing age-friendly cities. Drawing on interviews with older adults in three cities in the United Kingdom (UK), the analysis demonstrates that physical and social vulnerabilities, along with the characteristics of the built and social environment, play a role in influencing older adults’ behaviours, routines and habits in the community. The results are discussed with a view of influencing practice and policy priorities relating to age-friendly cities