Koopman Operators and the $3x+1$-Dynamical System

Leventides, John; Poulios, Costas

doi:10.1137/20m1348182

SIAM J. Appl. Dyn. Syst.

2021

DOI: 10.1137/20m1348182

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Koopman Operators and the $3x+1$-Dynamical System

John Leventides¹,

Costas Poulios²

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Cited by 2 publications

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“…Several attempts have been made after Lagarias' survey [13], and some offered equivalent formulations; see [4,10,6,3,9]. An operatortheoretic approach was presented in [14].…”

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confidence: 99%

Collatz map as a non-singular transformation

Assani

2024

Studia Math.

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Let T be the map defined on N = {1, 2, . . .} by T (n) = n/2 if n is even and T (n) = (3n + 1)/2 if n is odd. Consider the dynamical system (N, 2 N , T, µ) where µ is the counting measure. This dynamical system has the following properties:1. There exists an invariant finite measure γ such that γ(A) ≤ µ(A) for all A ⊂ N. For each functionWe also show that the Collatz conjecture is equivalent to the existence of a finite measure ν on (N, 2 N ) making the operator V f = f • T power bounded in L 1 (ν) with conservative part {1, 2}.

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“…Several attempts have been made after Lagarias' survey [13], and some offered equivalent formulations; see [4,10,6,3,9]. An operatortheoretic approach was presented in [14].…”

mentioning

confidence: 99%

Collatz map as a non-singular transformation

Assani

2024

Studia Math.

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Extended dynamic mode decomposition for two paradigms of non-linear dynamical systems

Leventides¹,

Melas²,

Poulios³

2023

Journal of the Franklin Institute

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Koopman Operators and the $3x+1$-Dynamical System

Cited by 2 publications

References 7 publications

Collatz map as a non-singular transformation

Collatz map as a non-singular transformation

Extended dynamic mode decomposition for two paradigms of non-linear dynamical systems

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