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Spectral conditions for chaos in cosine operator families

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  • Nafia, El-mahdi
  • Khoulane, Mohamed
  • Benmerrous, Abdelmjid
  • Elomari, M’hamed

Abstract

This paper is devoted to the study of chaotic behavior arising in families of cosine operators. We examine several forms of chaos, including distributional chaos and Li–Yorke chaos, within the framework of abstract evolution equations generated by cosine operator functions. By establishing appropriate spectral and dynamical conditions, we derive sufficient criteria ensuring the presence of chaotic dynamics. Our analysis highlights the intricate relationship between the underlying operator structure and the emergence of irregular temporal behavior. The results presented here extend and complement existing theories on chaos in linear dynamical systems, offering new insights into the long-term dynamics associated with higher-order evolution equations.

Suggested Citation

  • Nafia, El-mahdi & Khoulane, Mohamed & Benmerrous, Abdelmjid & Elomari, M’hamed, 2026. "Spectral conditions for chaos in cosine operator families," Chaos, Solitons & Fractals, Elsevier, vol. 208(P2).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p2:s0960077926003632
    DOI: 10.1016/j.chaos.2026.118222
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