Publications
Faculties » Faculty of Mathematics » Chairs » Mathematics VII - Analysis

Preprints

A. Abbondandolo, T. Rot,  On the homotopy classification of proper Fredholm maps into a Hilbert space , arXiv:1610.07039 [math.AT], 2016.

A. Abbondandolo, L. Asselle, G. Benedetti, M. Mazzucchelli, I. A. Taimanov,  The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere , arXiv:1608.03144 [math.DS], 2016. To appear in Adv. Nonlinear Stud.

A. Abbondandolo, B. Bramham, U. L. Hryniewicz and P. A. S. Salomão,  Sharp systolic inequalities for Reeb flows on the three-sphere , arXiv:1504.05258 [math.SG], 2015.

A. Abbondandolo, W. J. Merry,  Floer homology on the time-energy extended phase space, arXiv:1411.4669 [math.SG], 2014. To appear in J. Symplectic Geom.

Articles

A. Abbondandolo, L. Macarini, M. Mazzucchelli, G. P. Paternain,  Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level , J. Eur. Math. Soc. (JEMS) 19 (2017), 551-579.

A. Abbondandolo, B. Bramham, U. L. Hryniewicz and P. A. S. Salomão,  A systolic inequality for geodesic flows on the two-sphere, Math. Ann., Online First 2016.

A. Abbondandolo, O. Bernardi, F. Cardin  Chain recurrence, chain transitivity, Lyapunov functions and rigidity of Lagrangian submanifolds of optical hypersurfaces , J. Dyn. Diff. Equat., Online first 2016.

R. Darvishi Kamachali, A. Abbondandolo, K. F. Siburg, I. Steinbach, Geometrical grounds of mean field solutions for normal grain growth ,   Acta Materialia 90 (2015), 252-258.

A. Abbondandolo and P. Majer,  A non-squeezing theorem for convex symplectic images of the Hilbert ball, Calc. Var. 54 (2015), 1469-1506.

A. Abbondandolo and M.Schwarz, The role of the Legendre transform in the study of the Floer complex of cotangent bundles,   Comm. Pure Appl. Math. 68 (2015), 1885-1945.

A. Abbondandolo, L. Macarini and G. P. Paternain, On the existence of three closed magnetic geodesics for subcritical energies,   Comm. Math. Helv. 90 (2015), 155-193.

A. Abbondandolo and P. Majer, Global stable manifolds in holomorphic dynamics under bunching conditions Int. Math. Res. Notices vol. 2014 (2014), 4001-4048.

M. Abate, A. Abbondandolo and P. Majer, Stable manifolds for holomorphic automorphismsJ. Reine Angew. Math. 690 (2014), 217-247.

A. Abbondandolo and S. Matveyev,  How large is the shadow of a symplectic ball? J. Topol. Anal. 5 (2013), 87-119.

A. Abbondandolo and M. Schwarz, On product structures in Floer homology of cotangent bundles  in Global differential geometry", Springer Proceedings in Mathematics 17 (2012), 491-521.

A. Abbondandolo and M. Schwarz, Floer homology of cotangent bundles and the loop productGeometry & Topology 14 (2010), 1569-1722.

A. Abbondandolo and M. Schwarz, Estimates and computations in Rabinowitz-Floer homology,  J. Topol. Anal. 1 (2009), 307-405.

A. Abbondandolo and M. Schwarz, A smooth pseudo-gradient for the Lagrangian action functional,  Adv. Nonlinear Studies 9 (2009), 597-623.

A. Abbondandolo and P. Majer, Infinite dimensional Grassmannians,  Journal of Operator Theory. 61 (2009), 16-62.

A. Abbondandolo, A. Portaluri and M. Schwarz, The homology of path spaces and Floer homology with conormal boundary conditions,  J. fixed point theory appl. 4 (2008), 263-293.

A. Abbondandolo and P. Majer, A Morse complex for Lorentzian geodesics,  Asian Journal of Mathematics 12 (2008), 299-320.

A. Abbondandolo and A. Figalli, Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index,  J. fixed point theory appl. 3 (2008), 95-120.

A. Abbondandolo and A. Figalli, High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces,   J. Differential Equations 234 (2007), 626-653.

A. Abbondandolo and P. Majer, On the global stable manifold Studia Mathematica 177 (2006), 113-131.

A. Abbondandolo and M. Schwarz, On the Floer homology of cotangent bundles Comm. Pure Appl. Math. 59 (2006), 254-316.

A. Abbondandolo and M. Schwarz, Corrigendum: "On the Floer homology of cotangent bundles",   Comm. Pure Appl. Math. 67 (2014), 670-691.

A. Abbondandolo and P. Majer, A Morse complex for infinite dimensional manifolds Part I Adv. Math 197 (2005), 321-410.

A. Abbondandolo and P. Majer, When the Morse index is infinite Internat. Mat. Res. Not. 71 (2004), 3839-3854.

A. Abbondandolo and P. Majer, Ordinary differential operators in Hilbert spaces and Fredholm pairsMath. Z. 243 (2003), 525-562.

A. Abbondandolo, V. Benci, D. Fortunato and L. Masiello, On the Morse inequalities for geodesics on Lorentzian manifoldsMath. Res. Lett. 10 (2003), 435--445.

A. Abbondandolo, On the Morse index of Lagrangian systems Nonlinear Analysis 53 (2003) 551-566.

A. Abbondandolo and V. Benci, Solitary waves and Bohmian mechanics Proc. Nat. Acad. Sci. 99 (2002), 15257-15261.

A. Abbondandolo and P. Majer, Morse homology on Hilbert spaces Comm. Pure Appl. Math. 54 (2001), 689-760.

A. Abbondandolo and J. Molina, Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems Calc. Var. 11 (2000), 395-430.

A. Abbondandolo, Morse theory for asymptotically linear Hamiltonian systems Nonlinear Anal. TMA 39 (2000), 997-1049.

A. Abbondandolo, Subharmonics for two-dimensional Hamiltonian systems NoDEA Nonlinear Differential Equations Appl. 6 (1999), 341-355.

A. Abbondandolo, An H-theorem for a class of Markov processes Stochastic Anal. Appl. 17(1999), 131-136.

A. Abbondandolo, A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces Topol. Mathods Nonlinear Anal. 9 (1997), 325-382.

A. Abbondandolo, On the homotopy type of VMO Topol. Methods Nonlinear Anal. 7 (1996), 431-436.

A. Abbondandolo and V. Benci, Rotation numbers for Lagrangian systems and Morse theory Banach Center Publications 35(1996), 29-38.

A. Abbondandolo, Un indice medio per misure invarianti rispetto al flusso Lagrangiano Rend. Mat. Acc. Lincei 5 (1994), 213-221.


Monographs and lecture notes

A. Abbondandolo,  Lectures on the free period Lagrangian action functional,   J. fixed point theory appl. 5 (2013), 397-430.

A. Abbondandolo, L. Arosio, J. E. Fornæss, P. Majer, H. Peters, J. Raissy, L. Vivas,  A survey on non-autonomous basins in several complex variables , arXiv:1311.3835 [math.CV], 2015.

A. Abbondandolo, The minimax principle in the calculus of variations, in Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G. L. Naber, and Tsou S. T., Oxford: Elsevier 2006, volume 3, page 432-439.

A. Abbondandolo and P. Majer,  Lectures on the Morse complex for infinite dimensional manifolds, in  Morse theoretic methods in nonlinear analysis and in symplectic topology, pp. 1-74, NATO Science Series II: Mathematics, Physics and Chemistry, P. Biran, O. Cornea, and F. Lalonde Eds, Springer, 2006.

A. Abbondandolo and M. Schwarz, Notes on Floer homology and loop space homology, in  Morse theoretic methods in nonlinear analysis and in symplectic topology, pp. 75-108, NATO Science Series II: Mathematics, Physics and Chemistry, P. Biran, O. Cornea, and F. Lalonde Eds, Springer, 2006.

A. Abbondandolo, Morse theory for Hamiltonian systems, Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2001.

A. Abbondandolo,  Morse theory for strongly indefinite functionals and Hamiltonian systems, PhD Thesis, Scuola Normale Superiore, Pisa, 1999.