scholarly journals Equidistribution of divergent orbits of the diagonal group in the space of lattices

2018 ◽  
Vol 40 (5) ◽  
pp. 1217-1237 ◽  
Author(s):  
OFIR DAVID ◽  
URI SHAPIRA
Keyword(s):  
Euclidean Space ◽  
Life Span ◽  
Compact Set ◽  
Integer Vector ◽  
Entropy Methods ◽  
Numerical Invariants ◽  
Measure Rigidity ◽  
Higher Rank

We consider divergent orbits of the group of diagonal matrices in the space of lattices in Euclidean space. We define two natural numerical invariants of such orbits: the discriminant—an integer—and the type—an integer vector. We then study the question of the limit distributional behavior of these orbits as the discriminant goes to infinity. Using entropy methods we prove that, for divergent orbits of a specific type, virtually any sequence of orbits equidistributes as the discriminant goes to infinity. Using measure rigidity for higher-rank diagonal actions, we complement this result and show that, in dimension three or higher, only very few of these divergent orbits can spend all of their life-span in a given compact set before they diverge.

scholarly journals Rigidity properties for commuting automorphisms on tori and solenoids

2021 ◽  
pp. 1-46
Author(s):  
MANFRED EINSIEDLER ◽  
ELON LINDENSTRAUSS
Keyword(s):  
Complete Classification ◽  
Rigidity Theorem ◽  
Positive Entropy ◽  
Measure Rigidity ◽  
Higher Rank ◽  
Measurable Factors

Abstract Assuming positive entropy, we prove a measure rigidity theorem for higher rank actions on tori and solenoids by commuting automorphisms. We also apply this result to obtain a complete classification of disjointness and measurable factors for these actions.

Ergodic fractal measures and dimension conservation

2008 ◽  
Vol 28 (2) ◽  
pp. 405-422 ◽  
Author(s):  
HILLEL FURSTENBERG
Keyword(s):  
Dynamical Systems ◽  
Hausdorff Dimension ◽  
Euclidean Space ◽  
Ergodic Theorem ◽  
Compact Set ◽  
Linear Map ◽  
Compactly Supported ◽  
Almost Everywhere ◽  
Fractal Measures

AbstractA linear map from one Euclidean space to another may map a compact set bijectively to a set of smaller Hausdorff dimension. For ‘homogeneous’ fractals (to be defined), there is a phenomenon of ‘dimension conservation’. In proving this we shall introduce dynamical systems whose states represent compactly supported measures in which progression in time corresponds to progressively increasing magnification. Application of the ergodic theorem will show that, generically, dimension conservation is valid. This ‘almost everywhere’ result implies a non-probabilistic statement for homogeneous fractals.

Continuum of Care Following Sports-Related Concussion

2020 ◽  
Vol 29 (3) ◽  
pp. 1389-1403
Author(s):  
Jessica Brown ◽  
Kelly Knollman-Porter
Keyword(s):  
Young Adults ◽  
Life Span ◽  
Sports Injuries ◽  
Continuum Of Care ◽  
Medical Professional ◽  
Structured Interviews ◽  
Youth Athletes ◽  
Speech Language Pathologist ◽  
History Of ◽  
Injury Reporting

Purpose Although guidelines have changed regarding federally mandated concussion practices since their inception, little is known regarding the implementation of such guidelines and the resultant continuum of care for youth athletes participating in recreational or organized sports who incur concussions. Furthermore, data regarding the role of speech-language pathologists in the historic postconcussion care are lacking. Therefore, the purpose of this retrospective study was to investigate the experiences of young adults with history of sports-related concussion as it related to injury reporting and received follow-up care. Method Participants included 13 young adults with history of at least one sports-related concussion across their life span. We implemented a mixed-methods design to collect both quantitative and qualitative information through structured interviews. Participants reported experiencing 42 concussions across the life span—26 subsequent to sports injuries. Results Twenty-three concussions were reported to a parent or medical professional, 14 resulted in a formal diagnosis, and participants received initial medical care for only 10 of the incidents and treatment or services on only two occasions. Participants reported concussions to an athletic trainer least frequently and to parents most frequently. Participants commented that previous experience with concussion reduced the need for seeking treatment or that they were unaware treatments or supports existed postconcussion. Only one concussion incident resulted in the care from a speech-language pathologist. Conclusion The results of the study reported herein shed light on the fidelity of sports-related concussion care management across time. Subsequently, we suggest guidelines related to continuum of care from injury to individualized therapy.

Tumorigenesis in High-Dose Total Body Irradiated Rhesus Monkeys--A Life Span Study

2003 ◽  
Vol 31 (2) ◽  
pp. 209-213 ◽  
Author(s):  
Carel F. Hollander ◽  
Chris Zurcher ◽  
Johan J. Broerse
Keyword(s):  
Life Span ◽  
Rhesus Monkeys ◽  
High Dose ◽  
Life Span Study ◽  
Total Body

Conflict Monitoring Across the Life Span

2014 ◽  
Vol 28 (3) ◽  
pp. 124-135 ◽  
Author(s):  
Daniela Czernochowski
Keyword(s):  
Older Adults ◽  
Life Span ◽  
Age Groups ◽  
Conflict Detection ◽  
Response Conflict ◽  
Conflict Monitoring ◽  
Subsequent Performance ◽  
Additional Control ◽  
Performance Response ◽  
Conflict Detection And Resolution

Errors can play a major role for optimizing subsequent performance: Response conflict associated with (near) errors signals the need to recruit additional control resources to minimize future conflict. However, so far it remains open whether children and older adults also adjust their performance as a function of preceding response conflict. To examine the life span development of conflict detection and resolution, response conflict was elicited during a task-switching paradigm. Electrophysiological correlates of conflict detection for correct and incorrect responses and behavioral indices of post-error adjustments were assessed while participants in four age groups were asked to focus on either speed or accuracy. Despite difficulties in resolving response conflict, the ability to detect response conflict as indexed by the Ne/ERN component was expected to mature early and be preserved in older adults. As predicted, reliable Ne/ERN peaks were detected across age groups. However, only for adults Ne/ERN amplitudes associated with errors were larger compared to Nc/CRN amplitudes for correct trials under accuracy instructions, suggesting an ongoing maturation in the ability to differentiate levels of response conflict. Behavioral interference costs were considerable in both children and older adults. Performance for children and older adults deteriorated rather than improved following errors, in line with intact conflict detection, but impaired conflict resolution. Thus, participants in all age groups were able to detect response conflict, but only young adults successfully avoided subsequent conflict by up-regulating control.

Examining Relationships Across the Life Span

1997 ◽  
Vol 42 (2) ◽  
pp. 116-117
Author(s):  
Susan M. Profilet
Keyword(s):  
Life Span
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