## Banach Journal of Mathematical Analysis

### Conjugacy of P-configurations and nonlinear solutions to a certain conditional Cauchy equation

Orr Moshe Shalit

#### Abstract

We study the connection between conjugations of a special kind of dynamical systems, called P-configurations, and solutions to homogeneous Cauchy type functional equations. We find that any two regular P-configurations are conjugate by a homeomorphism, but cannot be conjugate by a diffeomorphism. This leads us to the following conclusion (answering an open question posed by Paneah): there exist continuous nonlinear solutions to the functional equation: $$f(t) = f\left(\frac{t+1}{2}\right) + f\left(\frac{t-1}{2}\right) \,\, , \,\, t \in [-1,1] .$$

#### Article information

Source
Banach J. Math. Anal. Volume 3, Number 1 (2009), 28-35.

Dates
First available in Project Euclid: 21 April 2009

http://projecteuclid.org/euclid.bjma/1240336420

Mathematical Reviews number (MathSciNet)
MR2461743

Zentralblatt MATH identifier
1157.39013

Digital Object Identifier
doi:10.15352/bjma/1240336420

Subjects
Secondary: 37B99: None of the above, but in this section

#### Citation

Shalit, Orr Moshe. Conjugacy of P-configurations and nonlinear solutions to a certain conditional Cauchy equation. Banach Journal of Mathematical Analysis 3 (2009), no. 1, 28--35. doi:10.15352/bjma/1240336420. http://projecteuclid.org/euclid.bjma/1240336420.

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