Chaos, Cycles, and Schwarzian Derivatives for Families of Asymmetric Maps

Julian I Palmore

Research output: Contribution to journalArticlepeer-review


We define dynamical systems of families of asymmetric maps on the unit interval. The asymmetric maps are derived by conjugation with Bernoulli Shifts, tent maps, logistic maps, and logistic shift maps. These maps are asymmetric Bernoulli Shifts, asymmetric tent maps, asymmetric logistic maps, and asymmetric logistic shift maps. We prove that these dynamical systems are chaotic and we compute invariant densities and Lyapunov exponents. We investigate properties of the Schwarzian derivatives in these families of functions.

Original languageEnglish (US)
Pages (from-to)235-242
Number of pages8
JournalApplicable Analysis
Issue number3-4
StatePublished - Aug 1 1995


  • asymmetric maps
  • discrete dynamical systems
  • Schwarzian derivatives

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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