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- Marcelo Sobottka
- 2006

In this paper we consider cellular automata (G, Φ) with algebraic local rules and such that G is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular automata and study the convergence of the Cesàro mean distribution of the iterates of any probability measure with complete connections and summable… (More)

- Eduardo Garibaldi, Marcelo Sobottka
- SIAM Journal of Applied Mathematics
- 2011

The ratio of males to females in a population is a meaningful characteristic of sexual species. The reason for this biological property to be available to the observers of nature seems to be a question never asked. Introducing the notion of historically adapted populations as global minimizers of maintenance cost functions, we propose a theoretical… (More)

- Daniel Gonçalves, Marcelo Sobottka, Charles Starling
- 2015

Recently Ott, Tomforde and Willis introduced a notion of one-sided shifts over infinite alphabets and proposed a definition for sliding block codes between such shift spaces. In this work we propose a more general definition for sliding block codes between Ott-Tomforde-Willis shift spaces and then we prove Curtis-Hedlund-Lyndon type theorems for them,… (More)

- Marcelo Sobottka, Luiz P. L. de Oliveira
- The American Mathematical Monthly
- 2006

- Marcelo Sobottka, Daniel Gonçalves
- J. Cellular Automata
- 2017

- Marcelo Sobottka, Daniel Gonçalves
- ArXiv
- 2015

In this note we propose an alternative definition for sliding block codes between shift spaces. This definition coincides with the usual definition in the case that the shift space is defined on a finite alphabet, but it encompass a larger class of maps when the alphabet is infinite. In any case, the proposed definition keeps the idea that a sliding block… (More)

- Eduardo Garibaldi, Marcelo Sobottka
- Mathematical biosciences
- 2014

This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose parameters are the secondary sex ratio (the ratio of males to females at time of birth), inter-, intra- and outer-gender… (More)

- Marcelo Sobottka
- ArXiv
- 2012

In this work we introduce the notion of weak quasigroups, that are quasigroup operations defined almost everywhere on some set. Then we prove that the topological entropy and the ergodic period of an invertible expansive ergodically-supported dynamical system with the shadowing property (X, T) establishes a sufficient criterion for the existence of… (More)

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