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Renormalization of Symmetric Bimodal Maps with Low Smoothness
Published in Springer
2021
Volume: 183
   
Issue: 2
Abstract
This paper deals with the renormalization of symmetric bimodal maps with low smoothness. We prove the existence of the renormalization fixed point in the space C1+Lip symmetric bimodal maps. Moreover, we show that the topological entropy of the renormalization operator defined on the space of C1+Lip symmetric bimodal maps is infinite. Further we prove the existence of a continuum of fixed points of renormalization. Consequently, this proves the non-rigidity of the renormalization of symmetric bimodal maps. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Figures & Tables (13)
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    Figure 1: Renormalization of a bimodal map
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    Figure 4: Intervals of next generations
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    Figure 3: Intervals of next generations
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    Figure 5: The combinatorics: (a) corresponding ... Expand
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    Figure 7: Length of intervals
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    Figure 8: (a), (b), (c) and (d) show the graphs of S0,l(c), ... Expand
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About the journal
JournalData powered by SciSpaceJournal of Statistical Physics
PublisherData powered by SciSpaceSpringer
ISSN00224715