Lyapunov Exponents, Periodic Orbits, and Horseshoes for Semiflows on Hilbert Spaces
نویسنده
چکیده
Two settings are considered: flows on finite dimensional Riemann-ian manifolds, and semiflows on Hilbert spaces with conditions consistent withthose in systems defined by dissipative parabolic PDEs. Under certain assump-tions on Lyapunov exponents and entropy, we prove the existence of geometricstructures called horseshoes; this implies in particular the presence of infinitelymany periodic solutions. For diffeomorphisms of compact manifolds, analogousresults are due to A. Katok. Here we extend Katok’s results to (i) continuoustime and (ii) infinite dimensions. Courant Institute of Mathematical Sciences, New York University, 251 MercerStreet, New York, New York 10012E-mail address: [email protected] Courant Institute of Mathematical Sciences, New York University, 251 MercerStreet, New York, New York 10012E-mail address: [email protected]
منابع مشابه
Some Non-hyperbolic Systems with Strictly Non-zero Lyapunov Exponents for All Invariant Measures: Horseshoes with Internal Tangencies
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