TY - JOUR
T1 - β- Expansion's attractors observed in A/D converters
AU - Kohda, Tohru
AU - Horio, Yoshihiko
AU - Aihara, Kazuyuki
N1 - Funding Information:
This research is supported by the Aihara Innovative Mathematical Modelling Project, the Japan Society for the Promotion of Science (JSPS) through the "Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)," initiated by the Council for Science and Technology Policy (CSTP).
PY - 2012
Y1 - 2012
N2 - The β-encoders, recently proposed analog-to-digital converters using an amplifier with factor βand a flaky quantizer with threshold ν have been proven to be explained as deterministic dynamics of "multi-valued Rényi-Parry maps." Such a map is locally eventually onto [ν-1, ν] which is topologically conjugate to Parry's (β, α)-map with α=(β-1)( ν-1). Switched-capacitor electronic circuits realizing the scaled ordinary and negative β-encoders lead us to observe their embedded attractors.
AB - The β-encoders, recently proposed analog-to-digital converters using an amplifier with factor βand a flaky quantizer with threshold ν have been proven to be explained as deterministic dynamics of "multi-valued Rényi-Parry maps." Such a map is locally eventually onto [ν-1, ν] which is topologically conjugate to Parry's (β, α)-map with α=(β-1)( ν-1). Switched-capacitor electronic circuits realizing the scaled ordinary and negative β-encoders lead us to observe their embedded attractors.
KW - A/D-converter
KW - Attractors
KW - Switched-capacitor circuit
KW - β-encoders
KW - β-expansion
UR - http://www.scopus.com/inward/record.url?scp=84867443982&partnerID=8YFLogxK
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U2 - 10.1016/j.piutam.2012.06.024
DO - 10.1016/j.piutam.2012.06.024
M3 - Conference article
AN - SCOPUS:84867443982
VL - 5
SP - 187
EP - 189
JO - Procedia IUTAM
JF - Procedia IUTAM
SN - 2210-9838
T2 - IUTAM Symposium on 50 Years of Chaos: Applied and Theoretical
Y2 - 28 November 2011 through 2 December 2011
ER -