Rapid evolution of complex limit cycles

The current article studies certain problems related to complex cycles of holomorphic foliations with singularities in the complex plane. We focus on the case when polynomial differential one-form gives rise to a foliation by Riemann surfaces. In this setting, a complex cycle is defined as a nontrivial element of the fundamental group of a leaf from the foliation. Whenever the polynomial foliation comes from a perturbation of an exact one-form, one can introduce the notion of a multi-fold cycle. This type of cycle has at least one representative that determines a free homotopy class of loops in an open fibered subdomain of the complex plane. The topology of this subdomain is closely related to the exact one-form mentioned earlier. We introduce and study the notion of multi-fold cycles of a close-to-integrable polynomial foliation. We also explore how these cycles correspond to periodic orbits of a certain Poincar\'e map associated with the foliation. Finally, we discuss the tendency of a continuous family of multi-fold limit cycles to escape from certain large open domains in the complex plane as the foliation converges to its integrable part.Comment: 44 page

Remembering Interactions with Others: The Role of Personal Intelligence and Personality

One relatively unexplored area in memory and personality research concerns the role that personal intelligence—i.e., a person’s ability to understand and reason about their own and others’ personalities—and personality traits may play in the way people think back to and remember their personal past. The current studies extended prior research by directly examining for the first time the relationship between personal intelligence, personality traits, and memory for specific aspects of the personal past. Across two studies, 391 participants (NStudy 1 = 141; NStudy 2 = 250) of different age groups completed a Qualtrics survey comprised of open-ended narrative prompts and close-ended questionnaires. The open-ended prompts allowed for an assessment of participants’ narrative content for two specific (one positive, one negative) memories involving another person, as well as descriptions of personal characteristics and those of other people. The questionnaires were used to measure self-rated functional usage and select qualities (e.g., perceived importance) of the memories, along with personal intelligence and personality traits. The results of both Study 1 and 2 revealed a significant relationship between level of personal intelligence and differences between participants in terms of their recalling and writing about person-centered information across all four narrative prompts, as well as participants’ memory function. The findings also indicated multiple correlations between personality traits and subjective qualities of memory for the personal past. The results are discussed in relation to their theoretical, empirical, and practical implications