Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Relativized problems with abelian phase group in topological dynamics.

D McMahon1

  • 1Department of Mathematical Sciences, New Mexico State University, Las Cruces, N.M. 88003.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1976
PubMed
Summary

This study introduces a new method for constructing minimal transformation groups using a function F. This allows for simplifying complex problems in topological dynamics by assuming the phase group is abelian.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Novel on-site follow-up and enhancement program (FEP) improves knowledge, clinical skills and enabling environment of skilled birth attendants in Nepal.

PloS one·2023
Same author

Venular amyloid accumulation in transgenic Fischer 344 Alzheimer's disease rats.

Scientific reports·2022
Same author

Gaining access to treatment; life at the far side of atopic eczema.

Clinical and experimental dermatology·2021
Same author

Teriparatide and pelvic fracture healing: a phase 2 randomized controlled trial.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2021
Same author

Surge in calls to Irish Skin Foundation's 'Ask a nurse' helpline during the COVID-19 pandemic.

Clinical and experimental dermatology·2021
Same author

Predictors of CNS injury as measured by proton magnetic resonance spectroscopy in the setting of chronic HIV infection and CART.

Journal of neurovirology·2014

Area of Science:

  • Topological Dynamics
  • Group Theory
  • Abstract Algebra

Background:

  • Equicontinuous minimal transformation groups are fundamental in topological dynamics.
  • The Cantor group (X = pi(infinity)Z(2)) and its associated group (S = [unk](infinity)Z(2)) serve as key structures.
  • Understanding group actions is crucial for analyzing dynamical systems.

Purpose of the Study:

  • To construct a function F: X x S --> T for any countable group T.
  • To demonstrate that the product space (X x Y, S) forms a minimal transformation group under a defined action.
  • To establish that homomorphisms between minimal transformation groups can be preserved under this construction.

Main Methods:

  • Construction of a novel function F: X x S --> T.
  • Definition of a new group action on the product space X x Y.

Related Experiment Videos

  • Utilizing properties of homomorphisms to prove the preservation of structure.

    • Main Results:

    • A method is presented to create a minimal transformation group (X x Y, S) from a given minimal transformation group (Y, T).
    • The constructed action preserves the homomorphism properties of the base group.
    • It is shown that for many problems in topological dynamics, the phase group can be assumed to be abelian without loss of generality.

    Conclusions:

    • The developed framework simplifies the study of topological dynamics by allowing assumptions about the phase group.
    • This work provides a valuable tool for analyzing and constructing minimal transformation groups.
    • The findings have implications for understanding the structure and properties of group actions in dynamical systems.