Defines the kernel of polynomial convolution on bisequences over R/Z and studies its similarities to the roots of the defining polynomial.
A link between Topological Entropy and Lyapunov Exponents
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abstract
We show that a $C^1-$generic non partially hyperbolic symplectic diffeomorphism $f$ has topological entropy equal to the supremum of the sum of the positive Lyapunov exponents of its hyperbolic periodic points. Moreover, we also prove that $f$ has topological entropy approximated by the topological entropy of $f$ restrict to basic hyperbolic sets. In particular, the topological entropy map is lower semicontinuous in a $C^1-$generic set of symplectic diffeomorphisms far from partial hyperbolicity.
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2025 1verdicts
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Dynamical systems defined by polynomials with algebraic properties
Defines the kernel of polynomial convolution on bisequences over R/Z and studies its similarities to the roots of the defining polynomial.