Irrational numbers | Dynamical systems
In the mathematical theory of dynamical systems, an irrational rotation is a map where θ is an irrational number. Under the identification of a circle with R/Z, or with the interval [0, 1] with the boundary points glued together, this map becomes a rotation of a circle by a proportion θ of a full revolution (i.e., an angle of 2πθ radians). Since θ is irrational, the rotation has infinite order in the circle group and the map Tθ has no periodic orbits. Alternatively, we can use multiplicative notation for an irrational rotation by introducing the map The relationship between the additive and multiplicative notations is the group isomorphism . It can be shown that φ is an isometry. There is a strong distinction in circle rotations that depends on whether θ is rational or irrational. Rational rotations are less interesting examples of dynamical systems because if and , then when . It can also be shown that when . (Wikipedia).
What are Irrational Numbers? | Number System | Don't Memorise
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From playlist Irrational Numbers
Irrational to Irrational power is rational? A classic Abstract Algebra Proof
Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Daddy is back with something different for once :3 Let us deal with a well known fact: Irrational to the power of an Irrational number can indeed be Rational! Let u
From playlist Number Theory
Irrational to Irrational Power is Rational?! Another Example!
GET 15% OFF EVERYTHING! THIS IS EPIC! https://teespring.com/stores/papaflammy?pr=PAPAFLAMMY Help me create more free content! =) https://www.patreon.com/mathable AC Playlist: https://www.youtube.com/watch?v=jmD1CWzHjzU&list=PLN2B6ZNu6xmdvtm_DdFUaHIK_VB84hG_m Daddy's back with some fancy
From playlist Advent Calendar 2018
Can an Irrational Number to Irrational Power be Rational?
Solution on Lemma: http://lem.ma/J7 Twitter: https://twitter.com/PavelGrinfeld
From playlist Problems, Paradoxes, and Sophisms
#2 Idenitfying Irrational numbers
An example that helps in identifying irrational numbers and understanding the basic concepts of irrational numbers.
From playlist Middle School This Year
From the creators of "e is irrational" comes now the proof that pi is irrational. This proof is originally due to Niven and only uses calculus, but it is very non-intuitive. That said, it is absolutely fascinating, so be prepared for a fun ride!
From playlist Cool proofs
a problem on irrational square roots
From playlist Common Core Standards - 7th Grade
Math Mornings: Chaos on the Circle, by Taylor McAdam
Rotate a circle by a fixed angle, then repeat again and again. Where will a single point travel? Will it come back to where it started and how does the answer depend on the rotation angle? Rotations and other transformations of the circle teach us a lot about many processes like planets
From playlist Math Mornings at Yale
Determine Rational or Irrational Numbers (Square Roots and Decimals Only)
This video explains how to determine if a given number is rational or irrational.
From playlist Functions
Gabriela Alexandra Estevez Jacinto: Hyperbolicity of renormalization for bi-cubic circle maps...
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 21, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Dynamical Systems and Ordinary Differential Equations
Anna Duwenig: Non-commutative Poincaré duality of the irrational rotation algebra
Talk by Anna Duwenig in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on September 9, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Irrational Numbers - What are they?
Learn what an irrational number is in this free math video tutorial by Mario's Math Tutoring. 0:07 What is an Irrational Number 0:11 What is an Integer 0:35 Example of a Rational Number 7 1:02 Example of How a Repeating Decimal is Rational 1:26 Example 1 is Square Root of 7 Rational? 1:40
From playlist Algebra 1
Boundary dynamics for surface homeomorphisms – Andres Koropecki & Meysam Nassiri – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.12 Boundary dynamics for surface homeomorphisms Andres Koropecki & Meysam Nassiri Abstract: We discuss some aspects of the topological dynamics of surface homeomorphisms. In particular, we survey recent results about
From playlist Dynamical Systems and ODE
Sigrid Grepstad: Bounded remainder sets for the discrete and continuous irrational rotation
Abstract : Let α ϵ ℝd be a vector whose entries α1,...,αd and 1 are linearly independent over the rationals. We say that S⊂𝕋d is a bounded remainder set for the sequence of irrational rotations {nα}n⩾1 if the discrepancy ∑Nk=11S({kα})−N mes(S) is bounded in absolute value as N→∞. In one di
From playlist Women at CIRM
Davoud Cheraghi: Arithmetic geometric models for the renormalisation of irrationally indifferent...
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Virtual Conference
Mitsuhiro Shishikura: Renormalization in complex dynamics
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 21, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
From Embedded Contact Homology to Surface Dynamics - Jo Nelson
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: From Embedded Contact Homology to Surface Dynamics Speaker: Jo Nelson Affiliation: Rice University; Member, School of Mathematics Date: February 27 2023 I will discuss work in progress with Morgan Weiler on knot filtered e
From playlist Mathematics
8ECM Invited Lecture: Stuart White
From playlist 8ECM Invited Lectures
Jörg Thuswaldner: S-adic sequences: a bridge between dynamics, arithmetic, and geometry
Abstract: Based on work done by Morse and Hedlund (1940) it was observed by Arnoux and Rauzy (1991) that the classical continued fraction algorithm provides a surprising link between arithmetic and diophantine properties of an irrational number αα, the rotation by αα on the torus 𝕋=ℝ/ℤT=R/
From playlist Dynamical Systems and Ordinary Differential Equations
π is Irrational: A Simple Proof 🥧
π is Irrational: A Simple Proof. A little basic calculus is all you need. Based on Ivan Niven's one-page proof: http://bit.ly/NivenPi My own rendition of Niven's proof: bit.ly/IrrationalPi [I wrote a book! https://amzn.to/3tI332x]
From playlist π 🥧